Skip to main content

Full text of "Topographic stadia surveying; a manual with reduction tables and a new type of reduction diagram"

See other formats


GIFT or 



C< t , /jjiUAy^J^ 




University of California • Berkeley 



J 1JEXLIBRIS 




TOPOGRAPHIC 

STADIA SURVEYING 

A MANUAL WITH REDUCTION TABLES 

AND 

A NEW TYPE OF REDUCTION DIAGRAM 



BY 

C. E. GRUNSKY, Eng.D. 

Mem. Am. Soc. C.E. 



18 ILLUSTRATIONS 
and A FOLDING PLATE 




NEW YORK 

D. VAN NOSTRAND COMPANY 

25 Park Place 

1917 



Copyright, 1917, by 
C. E. GRUNSKY 



[RFURY & # 



PREFACE 



The notes on Stadia Surveying, presented in this manual, 
were assembled a number of years ago. For the benefit 
of the surveyor who has occasion to use the telemeter they 
are now made available in printed form. The method of 
surveying herein described and the special type of diagram 
for the reduction of stadia notes, herewith supplied, have 
been found so satisfactory by the author, and by others 
who have tried them out, that he considers it a duty to give 
the profession the benefit of his experience. 

C. E. Grunsky. 

San Francisco, Cal., 
June 1, 1917. 



y aft 



CONTENTS 



STADIA SURVEYING 

CHAPTER PAGE 

I. Introduction and Definitions 1 

Theoretical Considerations 3 

The Porro Telescope 5 

II. The Stadia Formula 9 

Derivation of Formula 9 

Determination of the Rating Factor 10 

General Formulas for Inclined Sights 12 

Approximation Formulas 16 

Suggestions Relating to the Use of the Formulas 17 

III. Diagrams for the Reduction of Stadia Measure- 

ments 19 

Diagrammatic Solution of the Stadia Formulas 19 

The Diagram Furnished with this Manual 22 

IV. The Slide-rule as an Aid in Reducing Stadia Notes 24 

Modification of Formulas for Slide-rule Work . . 24 

V. Methods of Stadia Surveying 26 

Stadia Surveys without the Use of the Magnetic 

Needle 26 

Stadia Surveys with the Use of the Magnetic 

Needle 28 

VI. Practical Suggestions 30 

Departures from Ordinary Practice 30 

The Stadia Rod 30 

The Elimination of the Height of the Telescope 

above the Instrument Station Plug 35 

The Liberal Use of the Magnetic Needle 37 

v 



vi CONTENTS 

CHAPTER . PAGE 

Stadia Notes 38 

Note-book Sample Pages 40 

Vertical Angles Measured with an Alidade 44 

The Amount of Error when the Sighting Point 

does not Bisect the Intercept 44 

Table 1. Corrections for too Large a Ver- 

cal angle . . . 45 

Table 2. Corrections for too Small a Ver- 
tical angle 46 

The Amount of Error Due to Inclined Rod 47 

The Accuracy of Telemeter Surveys 48 

Table 3. Corrections for Departures cf the 
Stadia Rod from a True Vertical Posi- 
tion, etc 49 

Table 4. Corrections for Departure of the 
Stadia Rod From a True Vertical Posi- 
tion, etc 50 

The Effect of Refraction 51 

VII. The Platting of Stadia Notes 52 

VIII. Tables: 

Table 5. Values of e cos a and e sin a 54 

Table 6. Stadia Reduction Table 57 

Table 7. U. S. Geological Survey Tables for 

Obtaining Differences in Elevation 63 

Conversion of Feet into Miles 91 

IX. How to Use the Stadia Diagram 93 

Index 97 

Stadia Diagram in Cover Pocket 



TOPOGEAPHIC STADIA SUEVEYING 



CHAPTER I 
INTRODUCTION AND DEFINITIONS 

Telescope Cross-hairs, Adjustable or Fixed. The 

telescope to be used in stadia work is equipped with three 
horizontal cross-hairs. The spacing of these cross-hairs 
may be either adjustable or fixed. For general use the fixed 
cross-hairs are preferred by most engineers and surveyors, 
though they are not without their disadvantages. 

When the cross-hairs are adjustable frequent testing of 
the instrument rating may be necessary. 

When the cross-hairs are fixed (this term being here use in 
the sense of permanent in their relative positions, i.e., non- 
adjustable), the instrument's rating as reported by its 
maker should be carefully tested before any surveys requiring 
the limit of attainable accuracy are undertaken. 

Tachymetry. Tachymetry is that branch of surveying 
which deals with the rapid measurement of distances, as, for 
instance, the determination of distance from an instrument 
by sighting with its telescope to a rod. 

Telemeter. The term " telemeter " may be applied to 
any telescope equipped with cross-hairs for measuring dis- 
tance, or equipped with micrometer screw or other device 
for accurate determination of the length of rod subtended 
by an angle of known amplitude. (Only the instruments 
equipped with cross-hairs are taken into consideration in 



2 eV s , topographic Stadia surveying 

this discussion, as these alone have come into general use in 
topographic surveying). 

Stadia-rod or Telemeter-rod or " The Rod." These designa- 
tions are applied to the rod which is used in connection with a 
telemeter for measuring distance. The rod may be equipped 
with targets, or, as is more common, it may be a self-reading 
rod; that is to say, a rod on whose face the subdivisions 
and repetitions of the distance unit are so plainly indicated by 
markings and figures that the instrument-man can read the rod 
without recourse to targets. The use of a target-rod is a refine- 
ment not justified by the accuracy attainable with a telemeter 
and need not, therefore, receive any special consideration. 

Intercept. The intercept is the length of that portion of 
the rod, in stadia units, appearing between two cross-hairs, 
generally between the lower and the upper hairs. 

The Anallatic Point. The anallatic point of any instru- 
ment is that point from which the distance to a rod which is 
read for distance is proportional to the intercept. For an 
ordinary telescope the anallatic point lies a principal focal 
length in front of the object glass. 

The Telemeter Constant. This is a value to be deter- 
mined for each telemeter. It is, for an ordinary telescope, 
the sum of the principal focal distance of the object-glass 
plus the length of the part of the telescope from the 
instruments vertical axis to the object-glass. It is the dis- 
tance (measured along the collimation axis of the telescope) 
of the anallatic point from the vertical axis of the instrument. 

The Rod-reading. The rod-reading, as this expression is 
used in this manual, is one hundred times the intercept. 
Unless otherwise noted it is to be understood that an instru- 
ment rating of 100 is assumed. In other words one stadia 
unit on the rod is to be read and entered in the notes as 100. 

The Sighting Point. The sighting point on the rod is that 
point on the rod to which the sight is taken for vertical angles. 
It is the point on the rod on which the middle cross-hair is 
set for the vertical angle. 



TOPOGRAPHIC STADIA SURVEYING 3 

The Rating Factor. The rating factor of any instrument is 
that factor by which, when sighting horizontally to a vertical 
rod, the intercept (read in any linear unit as for example in 
feet), must be multiplied to find the distance to the rod 
(in the same linear unit), from the anallatic point. 

The Principal Focal Distance. The expression " principal 
focal distance " is the distance from a lens at which parallel 
rays of light passing through it are brought to a focus. 

The Stadia Unit. The stadia unit is a rod increment of 
such length that one such unit will be intercepted, when 
sighting horizontally, for each 100 or 200 or other number 
of units (depending on the rating factor of the instrument), 
that the rod is distant from the anallatic point. 

Theoretical Considerations. The object-glass of the 




I 

w— * ! 

Fig. 1. 

ordinary telescope of a transit or plane-table alidade is a 
convex lens. For every convex lens: 

1 1 * 
B + ' b =f (1) 

Here B is the distance from the lens to some object whose 
image appears on the opposite side of the lens at the distance 
b, and / is the principal focal distance of the lens. 

A horizontal sight being assumed, let S, Fig. 2, represent 
the intercept on a rod and s the actual space between 
the cross-hairs. Then 

&-*| (2) 



4 TOPOGRAPHIC STADIA SURVEYING 

Combining (1) and (2) 

I A -I. 

B + Bs~f 

Bs 

S+s=j; 



s 



(3) 




Fig. 2. 



The value of s and the value of / for any telescope are con- 



stant, therefore, - is a constant 
s 

Make 

/ 



K, 



Then 



B-f=KS. 



(4) 



The distance B—f, Fig. 3, is proportional to the inter- 
cept S. 

The relation between B—f, S, s and / expressed in Eq. (3) 
appears also from the optical principle illustrated in Fig. 3. 



TOPOGRAPHIC STADIA SURVEYING 5 

The Porro Telescope. It is practicable to construct a 
telescope in which the anallatic point will coincide with the 
vertical axis of the instrument. This fact was first demon- 
strated by an Italian officer, Mr. Porro, who, in 1823, con- 




k--/ 



--(B-f) 



Fig. 3. 



structed and described a telescope in which lenses were so 
combined that all rod-readings were proportional to the dis- 
tances from the center of the instrument. How this was 
done will appear by reference to Fig. 4. The object-glass 
and the auxiliary lens 0' are so placed that the vertical axis 




of the instrument, at C, is between them. The object-glass 
has a longer focal distance than that of the ordinary tele- 
scope. If the construction is such that the points C and ¥' 
are conjugate foci for the lens and the two lenses are rigidly 
connected, the angle at C will be constant. In other 
words, the intercept S will be proportional to the distance D, 



t> TOPOGRAPHIC STADIA SURVEYING 

Referring to this type of instrument, which has not come 
into use in this country, Mr. A. Lietz says:* 

" Since stadia measurements originate from the outer focus of 
the objective lens, and not from the center of the instrument, it 
becomes somewhat troublesome to apply a correction therefor on 
inclined sights, for, since the corrections remain constant for any 
distance and vary with the angle of inclination only, it is not 
practical to incorporate them directly into the tabular values em- 
ployed in reducing stadia observations. Such tables are usually 
augmented by placing the corrections due to what is generally termed 
the constant e at the bottom thereof. To overcome this difficulty, 
and to make every reading date directly from the center of the 
instrument, the Italian Porro invented a method in 1823, which is 
now beginning to be better known. This method has been fre- 
quently discussed. The Journal of the Franklin Institute contains 
an article in a number as far back as 1868. The Engineering News 
of November 8, 1890, has a short discussion by one of our best 
writers on these subjects, Prof. J. B. Johnson, of Washington Uni- 
versity, St. Louis. 

" A convex lens of required focal length is inserted between the 
objective and the eyepiece, which transfers the anallatic point to 
the occupied center. Theoretically this is necessary, for the observed 
vertical angles have their common vertex in the center of the arc, 
or horizontal axis of the telescope; while the vertex of the dias- 
timometric angle lies outside of the objective, a distance of 14 ins. 
from the center of the instrument in the ordinary large transit. 
This would cause slight errors in vertical angle and distance, which 
disappear in the Porro telescope. 

M There are very substantial reasons, however, why this anallatic 
lens has not found a more general application in modern surveying 
instruments, for it is not a new thing with which we are dealing, but 
a principle that was known and used over half a century ago; and 
these reasons will now be briefly considered. 

11 By inserting an additional lens the equivalent focal length of 
the objective is considerably decreased, and the power and capacity 
are thereby correspondingly lessened. To exemplify this, reference 
is made to an actual test of which the results were accessible to me. 
In this case the focal length of the objective equaled 13 £ ins., that of 
the inserted lens 5 ins. and the distance between them 9f ins. The 
equivalent focal length of the combination was, therefore, 7f ins. 
The image of the system lay 2\ ins. behind the anallatic lens, and 
its distance from the objective, therefore, 11 f ins. Here we notice 
* Journal Assoc. Engrg. Socs., Vol. 19, 1897, p. 256 et seq. 



TOPOGRAPHIC STADIA SURVEYING 7 

that the available focal length has been shortened by the lens com- 
bination 4 j ins., which is a direct loss of nearly 37%. An ordinary 
telescope with a focus of llf ins., possessing an eyepiece with one of 
5 in., would have a power of 23, while the Porro telescope under sim- 
ilar conditions shows only 15, indicating the same percentage of loss 
in power. There is, however, a slight gain in brightness with the 
same aperture of objectives, for the reason that the admitted light 
is concentrated in a smaller space. In order to make up for the loss 
in power, due to the anallatic lens, a more powerful eyepiece must be 
made use of. One with an equivalent focal length of ^ in. would 
about compensate the 37% loss, but the brightness of the image 
would not then be quite up to that of the ordinary telescope, since 
the middle lens will cause a slight loss of light by reason of reflection 
and absorption. This, however, might again be rectified by giving 
the objective a somewhat larger aperture. 

" While it is readily seen that a Porro telescope might be con- 
structed fully up to the capacity of our ordinary transit telescope, 
it is also apparent that much greater care and refinement would 
have to be resorted to to reach it, for it is very important that the 
entire mechanical work should be perfectly in harmony with the 
greater optical requirements. The tubes must be absolutely straight, 
the axes of the lenses must be identical and their principal planes 
normal thereto. Greater care must be exercised in the construction 
of the objective, it being necessary to correct therein for the aberra- 
tion due to sphericity and achromatism of the anallatic — which is 
usually a simple convex lens — if we would retain a clear and dis- 
tinct image. 

"It is a problem for the instrument maker to construct the Porro 
telescope so that there shall be no complicated parts, and no excess 
of cost to speak against it. The additional lens, whose focal distance 
depends upon the length of the telescope and the location of the 
center of the instrument, is placed in front of and not too far from 
the cross-hair diaphragm. Its distance from the objective must 
necessarily remain constant, and any motion of the latter in the tube 
must be made with the middle lens also. The lenses must move 
together. 

"It might be a more advantageous construction to adopt the mov- 
able eyepiece, and to focus by shifting the cross-hair diaphragm in 
connection therewith. 

"This lens combination has one peculiar advantage that must not 
be left unmentioned, which is that it requires but a very small tele- 
scopic slide movement to focus from long to short distances and vice 
versa. A range of half an inch may be sufficient to cover all the 
required lengths of sight. 



8 TOPOGRAPHIC STADIA SURVEYING 

"In building the tube, provision must also be made for readily 
removing the inner lens in order to clean it, which would probably 
be frequently required. The arrangements for this purpose must be 
so contrived that the lens may be replaced in its proper position and 
accurately adjusted to the required optical conditions. 

"Every feature goes to show that the mechanical work of such a 
telescope must be of the highest order, if it shall meet the demands 
made upon it. With the cheaper grade of surveying instruments a 
Porro telescope is an impossibility. 

"Granted that we have a Porro telescope fully up to the power 
and capacity of that of the simpler construction, there are the con- 
stant disadvantages of using a powerful microscope, which must 
be more or less fatiguing to the eyes of the observer; and the accumu- 
lation of dust on the inner lens, a difficulty that may lead to consid- 
erable trouble and annoyance. These reasons have been more than 
sufficient to prevent the anallatic telescope from being generally 
introduced and practically used. It is granted, however, that, as a 
precise instrument, it is perfectly within the reach of the optical 
and mechanical arts to build one that shall fully accomplish the 
translation of the anallatic point to the center of the instrument." 



CHAPTER II 

THE STADIA FORMULA 

Derivation of Formula. The value (B-f) in Eq. (4), 
for any ordinary telescope arranged as a telemeter is, as has 
been shown, proportional to the intercept S on a rod held 
vertically. In other words, sighting horizontally, the par- 
allel cross-hairs of the telescope will intercept a space on a 
rod proportional to the distance at which the rod is held 



from a point which lies an object-glass principal focal length 
in front of the object-glass of the telescope. 

Let c, Fig. 5, represent the distance measured along the 
tube of the telescope from the vertical axis or center of the 
instrument to the object-glass. 

Then for a horizontal sight 

D=B+c; (5) 

or 

D = (B-f)+(c+f) (6) 

D=Ks + (c+f) (7) 

c+f=e, (8) 



From (4) 
Calling 



10 TOPOGRAPHIC STADIA SURVEYING 

which is allowable because the value c, being affected only 
by the movement of the object-glass in focusing upon the 
rod is for practical purposes to be regarded as a constant, 
Eq. (7) becomes 

D=e+KS (9) 

This is the fundamental formula. K is called the rating 
factor and e may for convenience be called the instrument 
constant. 

The values of c and of /, and, therefore, the value of e, 
can always be directly measured with sufficient precision; / 
in the instrument of the ordinary type with single objective 
is the length of that portion of the telescope tube between the 
objective glass and the cross-hairs, when the telescope 
has been focused upon a distant object. The value of c 
may be determined also by measurement when the tele- 
scope is focused upon some object about 50 ft. distant. 

Determination of the Rating Factor. When a telescope 
has fixed cross-hairs and the value of e has been ascertained 
the instrument's rating factor is determined as follows : 

Measure from the vertical axis of the instrument as follows: 

To point Pi at (100+6) ft.; 
To point P 2 at (200 +e) ft.; 
To point P 3 at (300 +e) ft.- 

etc. etc. 

To point, Pio at (1000 +e) ft. 

The selected ground for such a determination must be 
such that all of the readings can be made with a horizontal 
telescope otherwise the rod must be held normal to each line 
of sight and the distance measured on the ground must be 
parallel with this line of sight. 

The rod being held at each of the ten points there will be 
obtained ten rod readings (each foot on the rod being read 
as 100 ft.). These readings are now divided in their order 
by 1, 2, by 3, etc., by 10. Each quotient will be an observed 



TOPOGRAPHIC STADIA SURVEYING 11 

value of the instrument's rating-factor. The mean of the 
observed values is to be accepted as the value of K. No 
individual observation should vary more than 0.2% from the 
mean. 

The stadia unit is then -— ft. 
A 

For example: Suppose K =80 then Vo 0- = 1-25 ft., the stadia 
unit. If now a rod based on the subdivision of 1.25 ft. in- 
stead of 1 ft. as the unit be prepared for use with the tele- 
scope whose stadia unit is 1.25, then each such unit may be 
read as 100 ft. 

Calling the stadia unit u, its value is 



but 
therefore 



100 

*«.£-; (io) 



D=e+KS; (9) 



D=e+100- (11) 

u 



The distance in feet, in other words, will be the instru- 
ment constant plus 100 times the intercept measured in stadia 
units. 

Whenever a rod has a stadia-unit other than one foot, some 
scheme of rod subdivision and marking should be used that 
will enable an easy identification of the rod, which is in this 
event to be used only with a particular instrument, and only 
for stadia and vertical angle work — not for any ordinary 
leveling. 

When the cross-hairs of the telescope are adjustable they 
can be set so that the rating of the instrument will be con- 
venient, usually 1 to 100. 

To adjust the cross-hairs measure from the center of the 
instrument to a distance about equal to the average length 
of a sight making the same some multiple of 100 ft. in- 



12 TOPOGRAPHIC STADIA SURVEYING 

creased by the instrument constant as, for instance (400 +e) ft. 
The cross-hairs are now so adjusted that the intercept 
between the lower and the upper hairs when sighting with a 
horizontal telescope will be exactly 4 ft. and that the middle 
cross-hair will exactly bisect this intercept. The rating of 
the instrument is thus made 1 to 100. If so convenient a 
rating factor as 100 is not practical the cross-hairs may, of 
course, be so adjusted that the intercept will have to be 
multiplied by some other round number — such as 50, 150 or 
200 — to make the product 400. 

After the cross-hairs have been adjusted with the rod at 
some such distance as (400 +e), or (500 +e), or (600 +e) ft., 
readings should be taken at other measured distances, as for 
example at one-half the distance first selected and at a point 
at twice this distance, in order to give a check upon the 
accuracy to be expected. The error in an individual sight 
for adjustment under assumed favorable atmospheric con- 
ditions, should not exceed 0.2%, if the instrument is intended 
for use in ordinary topographic surveying. 

It may be repeated that, for the instrument with fixed 
cross-hairs, either the rating factor must be determined, as 
explained, and used in estimating distances from readings 
on a rod with the measuring unit (one foot), as the subdi- 
vision unit, or in the manner already described the stadia 
unit is calculated from observations and a special rod is 
constructed for use with that instrument only. The latter 
is rarely a desirable procedure. 

General Formulas for Inclined Sights. When the transit, 
or the alidade of the plane-table are used to measure both 
distance and difference in elevation, the rod may be held 
either normal to the line of sight or vertical. In the first 
case the length of the inclined line from the instrument to 
the sighting point on the rod is measured. In the second case 
a reading is obtained from which the horizontal distance 
to the rod and the difference in elevation may be calculated. 
The advantages, for all ordinary surveying, of the second 



TOPOGRAPHIC STADIA SURVEYING 



13 



method, as illustrated in Fig. 6, are so pronounced that it is 
not necessary to discuss the use of the inclined rod. 

In Fig. 6 the intercept on a rod held vertically at the point 
P is S. The vertical angle, when the middle cross-hair is 
set on the sighting-point P' , is a. 

It is to be remembered, as already stated, that throughout 
this manual, except when otherwise noted, instruments 
rated 1 to 100 are referred to. For such instruments the 



i 

i 



I 



fc- : 



• 2D 



Fig. 6. 



rod-reading, as entered in the notes of the surveyor, will 
be 100 S. When instruments have some other rating the 
value KS may be substituted for the rod-reading (i.e., for 
100 S.) 

Referring again to Fig. 6, it will be seen that if the rod had 
been held through the point P' normal to the axis of the 
telescope, the intercept would have been HH', instead of S. 
The length of HH' establishes the length of the inclined 
line IP', and the line IP' together with the vertical angle 



14 TOPOGRAPHIC STADIA SURVEYING 

a. enables a calculation of the horizontal distance D and of the 
difference of elevation h to be made. 

HH' =S cos a (very nearly); .... (12) 

IP' = 100 S cos a +e; (13) 

Z> = (100£cosa=+e) cosa; . . . (14) 
and 

h = (100 S cos a +e) sin <*. ... (15) 

Calling the rod reading 

100 S=r; (16) 

D=r cos 2 a +e cog a; (17) 

h=r sin a cos a+e sin «; .... (18) 

h=r(% sin 2a)+e sin a (19) 



will make 



which is 



These are the formulas in ordinary and in general use for 
the determination of distance and difference in elevation 
with a stadia instrument. They are not strictly correct, 
because Eq. (12) is not mathematically correct. The line 
HH' normal to the collimation axis of the telescope is not 
normal to the two lines IH and IH', between which the inter- 
cept lies. These lines in the case of an instrument rated at 
100 enclose an angle of about 34'. Each of these lines departs 
from the line of sight by about 17'. It follows that while 
HP' is exactly equal to H'P' the intercept S is not exactly 
bisected by the middle cross-hair, there being in the small 
triangle BHP' and B'H'P' (see Fig. 7) an acute angle at H 
of about 89° 43 r , while at H' in the other small triangle the 
angle is obtuse, 90° 17'. 

It can readily be shown that the error made in accepting 
Eq. (12) is so small that it is negligible. In order that this 
may become apparent the following is presented. Referring 



TOPOGRAPHIC STADIA SURVEYING 



15 



to Fig. 7, draw the lines HA and H' A' perpendicular to HH' 
then 



HA =H'A'=- sin <*. 
2 




(20) 



Fig, 7. 



In the triangle HA B the angles will be, for an instrument 
rated at 100: 

At#, 17'; 
At A, 90° -a; 
At£, 90°+«-17'. 

In the triangle H'A'B' the angles will be 

AtH', 17 r ; 

At A', 90° +«; 

At£',90°-«-17'. 



Therefore 



. n S . sin 17' 

AB =- sin a ; 

2 sin (89° 43' -fa) 



(21) 



16 TOPOGRAPHIC STADIA SURVEYING 

a,t>, S . sin 17' 

4'£'=- sin a ; . . . (22) 

2 sin (89° 43' -a) V } 

and because 

tf#' = (S-A'£'+A£)cosa; .... (23) 

TJTJt o l\ sin a sin 17'/ 1 1 M ,„,, 

HH'-Scosa [l SL^———-. ______^. (24) 

and 

rv/ in no 9 l\ sin a sin 17'/ 1 1 \"| 

+e cos a. . (25) 

The error that results in using formula (14) or (17) in place 
of formula (25) will be 

O - O ^ 10 S co.4^^( 8ia(89 i 43 ,_ a) - sin(89 i 43 , +g) )]. C26 ) 

Based on this equation it appears that the inaccuracy of 
Eq. (17) is as follows: 
For 

a = 10° the error will be only .00007%; 

a =20° the error will be only .0003%; 

a = 30° the error will be only .0008%; 

a =45° the error will be only .0025%. 

These errors are, as already stated, too small to be taken 
into account. 

Approximation Formulas. The value of e is generally 
small. It will rarely exceed 2 ft. and will generally be nearer 
1 ft. This being the case there will be only a slight error 
introduced if in formulas (17) and (18) the value e be replaced 
by e cos a. This substitution is certainly allowable in all 
ordinary topographic surveying operations, in which dis- 
tances are required only to the nearest foot. 



TOPOGRAPHIC STADIA SURVEYING 17 

With this modification the formulas (17) and (18) become 
D = (r +e) cos 2 a (approximate) ; . . . . (27) 
h = (r+e) sin a cos a (approximate). . . (28) 

In this form the formulas are very convenient. 

The expressions (r+e) cos 2 « and (r+e) sin a cos a in 
these equations and the expressions r cos 2 a and r sin a cos a 
in Eq. (17) and (18) are such that they can conveniently 
be obtained from diagrams, as will hereinafter be explained. 

The practice of disregarding entirely the distance incre- 
ment e cos a in formula (17), and the elevation increment 
e sin a in formula (18) can not be endorsed. Although, 
as is well known, the error of the individual moderately long 
sight is frequently in excess of the value of e, the effect of 
ignoring the correction altogether would be cumulative, a 
source of error which is not allowable when locating primary 
or secondary stations. 

There is less objection to doing this when side shots for 
ground elevation only are involved. In this case the author's 
practice has always been to enter the reduction diagram, 
hereinafter described, with a value (r+1). One foot is a 
sufficiently close approximation of the value of e for all 
ordinary surveying instruments. 

For unimportant side shots, such as shots for elevation 
of the ground, the following approximations can therefore 
be recommended: 

D = (r + 1) cos 2 a; (29) 

h = (r + 1) sin a cos a. (30) 

Suggestions Relating to the Use of the Formulas. 
In reducing the field observations it will be well to be guided 
by the following suggestions: 

1. Use the correct formulas (17) and (18) in making sur- 
veys which- require the greatest attainable accuracy. 



18 TOPOGRAPHIC STADIA SURVEYING 

2. Use the approximation formulas (27) and (28) and 
stadia reduction tables for foresights and backsights and for 
sights to reference points. 

3. Use the approximation formulas (27) and (28) or (29) 
and (30) and a slide rule or such diagrams as accompany 
this manual for all ground heights and general topography. 

In order that the accuracy attainable by use of the approx- 
imation formulas (27) and (28) may be correctly gaged, it 
is to be stated that their use introduces errors as follows: 

When e = 1.5 ft. the error in distance will be less than 0.1 
ft. for all vertical angles less than 20°; it will be —0.2 ft. 
for a vertical angle of 30°, and —0.3 ft. for a vertical angle 
of 45°. The error in elevation will be less than 0.1 ft. for all 
vertical angles less than 30° and it will be —0.3 ft. for a 
vertical angle of 45°. 

For values of e other than 1.5 ft. the errors can readily be 
approximated from the foregoing, as they increase or decrease 
proportionately with e. 



CHAPTER III 

DIAGRAMS FOR THE REDUCTION OF STADIA 
MEASUREMENTS 

Diagrammatic Solution of Stadia Formulas. The fol- 
lowing considerations have led to the preparation of diagrams 
for the determination of values for the expressions r cos 2 a. 
and r sin a cos a in Eq. (17) and (18), (r+e) cos 2 a and (r+e) 
sin a cos a in the approximation formulas (27) and (28) and 




for the expressions (r+1) cos 2 a and (r+1) sin a cos a in the 
approximation formulas (29) and (30). 
In any circle whose radius is OP, Fig. 8, there will be 

IP =IL cos a; 
1P'=IL cos 2 a; 
PL =IL sin a: 
PP' =IL sin a cos a. 

If IL, the diameter of the circle be made equal to r or. to 
(r+e) or to (r+1), according to the formulas to be used, 

19 



20 



TOPOGRAPHIC STADIA SURVEYING 



^ ^ ^ 



O CJ <=> o 



45 




r— 1 1— — I 

STAniA 


1 1 1 ■ 

FIT AdU A\1 


[ 




£>• 




T"" 








145 


40 


— . For Instruments rated 1 to lOO 

EE Graphical Solution of the Approximation Formulas:— 












r-v^ 




^siNi 


140 


35 
















s?i§ 


135 










30 
25 

20 


~ D=(r + e)cosV D=(r+1)cos' 1 j 
~ h=(r+e) since cosct h = (r+l) since cosct - 

~. Where: £= 












*" .■ ■ 


-;-;: 








130 
125 
120 


15 

10 


— 0C= vertical angle. 

— D=horizontaI distance. 
EC h=difference in elevation. 

ZZl e=instrument constant=the distan 

ZZl of the outside focal point of the 

object lens from the instrument 

ZZ Directions:— 


Jt 










: 


^ 


/"' >~ 










115 
110 
105 


05 






\-f^jf-f-> 


/ v." 


/ / ,~ 
















100 
95 
90 
85 




W^ 




















95 


Follow the vertical angle ray to 

— the curved line fr-e) or (r-1) J 
— • as the case may be and read Z 

— D on the honzontal scale - 
and h on the vertical scale. ZZZ 


JH 




;;_ 




^ 


eg 














gc 






^^ 


; - 


'*> 


- \ 




80 


— NOTE:— The diagram can 

— also be used to find the 










^7%6^. 




~7 


-/ 1 


X 


s_v_ 








80 


75 
70 
65 

60 
55 
50 







rsin 


icon 








^-:V 


■ ' ■; 


















!3jj2j 

v., 




75 
70 
65 
60 
55 
50 


45 
40 
35 
30 
25 
20 
15 
10 
5 








i^L 


., 


.;;..; 


;>-' 




-/'-J 




* 


"7- 






gEI 






j^'l 


^3 

r 5 4 




45 
40 
35 
30 
25 
20 
15 
10 
5 



o o o o 



o — r-o t>J 
o O o 



<z> <z> <z> o cz> o o 



Fig. 9. 



TOPOGRAPHIC STADIA SURVEYING 21 

the line IP' will represent the distance increment and 
PP' the difference of elevation increment in the above 
formulas. 

If, now, for all possible values of r, or of (r+e), or of (r+1) 
as the case may be, a series of semicircles be drawn all 
having a common point 7, each circle will be the focus of the 
points P determined by all possible values of the vertical 
angle and a value of r, or of (r+e), or of (r+1), equal to the 
diameter of each circle. In other words, for any vertical 
angle a. the limiting side line of the angle, or the angle ray, 
will cut the circle at a point P such that the horizontal line 
IP' or I'P will be the value as the case may be of r cos 2 a, or 
of (r+e) cos 2 a, or of (r+1) cos 2 a, and that PP' will be the 
value of r sin a cos a, or of (r+e) sin a cos a, or of (r+1) sin 

a COS a. 

Semicircles with diameters increasing by regular amounts 
1 ft., or 2 ft., or 5 ft., or 10 ft., according to scale, and hori- 
zontal lines forming a scale by which to read off difference in 
elevation and vertical lines by which to read off distance, 
complete the diagram. 

To secure accuracy in scaling difference in elevation the 
unit of the vertical scale may be made larger than the unit 
of the horizontal scale. The semicircles will then be ellipses. 
According to the scales adopted any reasonable degree of 
accuracy can be attained. (See Fig. 9.) 

For ordinary topographic surveying the stadia diagram 
accompanying this manual will be found adequate to fill 
every requirement. This diagram is so arranged that both 
difference in elevation and correct horizontal distance can 
be read at the same point. The diagram has been drawn, 
in the main, to logarithmic scales in order that, for practically 
all distances the relative accuracy of results obtained by its 
use will be substantially the same. The distances shown on 
the diagram- are from 100 to 1000 feet. They might have 
been called 10 to 100 or 1 to 10 feet with a corresponding 
modification of the difference in elevation. The scale from 



22 TOPOGRAPHIC STADIA SURVEYING 

100 to 1000 feet was adopted because the largest number of 
sights will ordinarily fall between these limits. 

The curved lines in the diagram represent all possible 
values of r, of r+e, or of r+1. 

In using the diagram the same care must be exercised in 
placing the decimal point correctly as in the case of slide 
rule work. It is to be noted that in any region in which oro- 
graphic features are pronounced it would be useless to 
attempt to measure elevations with greater precision than 
to the nearest foot. They may, of course, be read from the 
diagram and entered in the notes to tenths, but should in 
such case appear on the map without fractional feet. 

The Diagram Furnished with this Manual. The dia- 
gram for the reduction of stadia notes which accompanies 
this manual is prepared specifically as a graphic solution at 
one operation of the approximation formulas. 

D = (r+e) cos 2 «; (27) 

and 

h = (r+e) sin a cos a. . . . (28) 

But the diagram may also be used in ascertaining the 
values of r cos 2 a and r sin a cos a in the correct formulas Eq. 
(17) and (18) and for the approximation of (r+1) cos 2 a and 
of (r+1) sin a. cos a in the approximation formulas (29) and 
(30). As the formulas (17) and (18.) need only be used for 
sights to turning points and on surveys requiring more than 
ordinary precision, it would seem advisable to give prefer- 
ence to reduction tables whenever such approximation for- 
mulas as (27) and (28) or (29) and (30) will not serve. 

To Use the Diagram. Follow the ray which corresponds 
to the angle « of elevation or depression to its intersection 
with the curved line which corresponds to the value (r+e) 
in formulas (27) and (28). Holding a needle point at the 
intersection thus determined read off on the vertical lines 
the horizontal distance D, that is (r+e) cos 2 a, and on the 



TOPOGRAPHIC STADIA SURVEYING 23 

horizontal lines the difference in elevation h, that is (r+e) 

sin a COS a. 

Thus when the approximation formulas are to be used, the 
diagram gives at once the distance and the difference in 
elevation for any rod-readings and any vertical angles 
within their scope. Distance should be read to the nearest 
foot and difference in elevation to the nearest tenth of a foot. 

When points are located by the intersection of sights from 
two instrument stations, the horizontal distances from each of 
these two stations are scaled from the map. The diagram is 
now entered with each of these distances and needle points 
are placed at the intersection of these distances with the 
corresponding angle rays of the measured angles of elevation 
or depression. If the same difference of elevation is not 
indicated by both needle points the mean value should be 
recorded. 



CHAPTER IV 

THE SLIDE-RULE AS AN AID IN REDUCING 
STADIA NOTES 

Modification of Formulas for Slide-rule Work. It is 

not always convenient to use a diagram in reducing rod- 
readings and vertical angles to distance and elevation dif- 
ference. This is particularly true for plane-table work 
which requires that the reduction be made in the field. In 
such cases slide-rules may be used to advantage. Special 
slide-rules are made for the purpose. These need not receive 
any special notice. But the ordinary slide-rule can be made 
a convenient aid as will now be shown. 

Formulas (17) D =r cos 2 «+e cos «; 

(18) h =r sin a cos «+ e sin a; 
and (27) D = (r +e) cos 2 a (approximate) ; 

(28) h = (r +e) sin « cos a (approximate) ; 

can be made convenient for solution with the slide-rule by 
substituting for sin a cos a. the trigonometric equivalent 

sin a cos a =^ sin 2« (31) 

For work with the slide-rule only the approximation for- 
mulas (27) and (28) or (29) and (30) should be used. 

24 



TOPOGRAPHIC STADIA SURVEYING 25 

In combination with (31) the Eqs. (27) and (28) will 
become : 

D = (r+e) cos 2 a; (27) 

t r + e • o 

h=— — sin 2a. 

Both of these equations or similar equations containing 
the factor (r+1) are readily solved with the ordinary slide- 
rule. 



CHAPTER V 
METHODS OF STADIA SURVEYING 

Stadia Surveys Without the Use of the Magnetic 
Needle. When the plane-table or transit are oriented 
without the use of a magnetic needle, the instrument is to 
be set up over a starting point of known position and eleva- 
tion. The height i of the telescope above the bench-mark or 
station-plug is measured and the table or transit are oriented. 
The first orientation is adapted to the shape of the area to 
be covered or to other considerations. It may, of course, be 
based on a north point determination. At all subsequent 
settings the plane-table or the lower plate of the transit, as 
the case may be, must be brought into a position parallel 
with the first setting. To accomplish this in the case of the 
transit, after setting the vernier at the azimuth which was 
read at the last station (when sighting toward the new sta- 
tion), and reversing the telescope, a sight is taken back toward 
the last station, whereby the lower plate of the transit is 
brought into the desired position. In the case of the plane- 
table the operation is similar, the ruler of the alidade being 
reversed along the last station sight. 

At each setting the height i of the telescope above the 
station plug is measured. This height determines the eleva- 
tion of the telescope the " height of instrument " in case this 
should be required. Ordinarily, this will not be required, all 
sights being taken for vertical angles to the point i on the rod 
as determined for each instrument setting. Differences in 
elevation as then determined, regardless of the value of t, 
are thereupon applied directly to the plug elevation of the 

26 



TOPOGRAPHIC STADIA SURVEYING 27 

instrument station. Only when level sights are taken and 
the rod is read direct for elevation will it be necessary to 
apply the readings to the height of instrument, which is, 
of course, the elevation of the station plug plus i. 

The rule should be carefully observed to let the last sight 
recorded at any station be the sight to the next station to be 
occupied. 

From each station as occupied there will first be the orien- 
tation of the transit or plane-table. In sighting back upon 
the last station occupied the rod should again be read for 
distance and the vertical angle should be noted. The survey 
is thus checked. The mean of the two observations, if there 
be no palpable error, should be used in determining position 
and elevation of the new station. 

As a variant of the foregoing the transit may be used at 
each station to determine the azimuth of all sights taken in 
their relation to the backsight. In this case the vernier is 
set at zero when taking the backsight for orientation. 

Each instrument station should be at such distance from 
the preceding — topographic features being considered — 
that it will command a fair amount of new territory. A 
foresight of the length of ordinary sights for topographic 
points would place the new station at the margin of the terri- 
tory already commanded. In some cases it may be advisable 
simply to make the foresight as long as consistent with the 
accuracy required. In other cases it may be of advantage 
to treat alternate stations as secondary stations using them 
only for the purpose of locating the next primary station 
farther on. 

Referring to stadia surveys, Noble and Casgrain, in the 
introduction to their tables for horizontal distance and 
difference of level,* say: "The height of instrument can be 
determined from the backsight, or the instrument can be 
set over a point whose height has been determined and the 

* A. Noble and W. T. Casgrain. Tables for Horizontal Distance 
and Difference of Level. Eng. News Pub. Co., 1902. 



28 TOPOGRAPHIC STADIA SURVEYING 

height of the telescope above it is measured directly by a 
light graduated rod carried for the purpose. The latter is the 
usual method." 

Stadia Surveys with the Use of the Magnetic Needle. 
When the magnetic needle (or a solar compass) is used 
in orienting the transit or the plane-table, or in determining 
the azimuth of the sights taken with the transit, a different 
method of surveying is made possible. The intermediate 
or secondary stations can be treated as turning-points. 

The instrument is not set up at all at the secondary stations. 
But, in this case, the double sighting between stations is no 



longer possible and recourse should be had to some other 
method of checking the observations. Probably the best 
method of accomplishing this is by using two intermediate 
stations, preferably so selected that the angle between the 
two foresights to these stations will be at least 30°. As all 
stadia work should be done with two or more rodmen there 
is usually no difficulty in adopting this double-turning-point 
method. Two locations and two elevations of each primary 
station will thus be obtained. Barring gross .errors, the 
mean of the elevations and of the positions of the new instru- 
ment station thus determined should be accepted. (Correc- 
tions can be carried back, if desired, to the two secondary 
stations.) 



TOPOGRAPHIC STADIA SURVEYING 29 

Fig. 10 illustrates a set of sights of this kind. The broken 
lines show the sights as taken; the full lines as they will 
appear when corrected. 

The method of keeping notes for a transit survey by the 
double-turning-point method is illustrated on page 40. 



CHAPTER VI 

PRACTICAL SUGGESTIONS 

Departures from Ordinary Practice. The author has 
found several departures from the ordinary methods of 
stadia surveying advantageous and recommends them to 
those who have occasion to use the stadia. These depar- 
tures, including some modifications of methods already 
alluded to, relate: 

1. To the type of rod. 

2. To the elimination from the notes of the height of the 
telescope above a station plug. 

3. To the liberal use of the magnetic needle. 

4. To the method of keeping field notes. 

5. To the use of approximation formulas. 

6. To the use of convenient stadia reduction diagrams. 
The Stadia Rod. The rod which is here described was 

designed and its markings were devised about 1880 in the 
office of the State Engineer * of California. No one will be 
surprised or misled when the author, under whose super- 
vision the first rod of the kind was made, states that he has 
found no other self-reading rod equally satisfactory for gen- 
eral use. The rod is presented on its merits, without prejudice 
to other self-reading rods of which many more or less satis- 
factory types are on the market. 

The rod is shown in Figs. 11 to 16. It is a folding rod, 
being cut midway of its length, so that, when folded, the 
painted face of the rod will be protected against injury. 

*Wm. Hammond Hall was at that time the State Engineer of 
California. 

30 



TOPOGRAPHIC STADIA SURVEYING 



31 



Stiffness when extended is secured by means of a light board, 
Fig. 11, with projecting overlapping edges. The hinges are 
relieved of all strain by this arrangement. 

Into the back of the stiffening board are set two small 
plates of iron with round holes through which, and through 





B 



i ^ 



Fig. 11.— The stiffen- 
ing board. 



I 
I 

D 



Fig 12. 



Fig. 13.— The folded 
rod. 



the board and through the rod, thumb-screws pass to similar 
plates with threaded holes in the face of the rod. 

The type of thumb-screw to which preference has been 
given by the author was turned from a round bar of iron, 
as shown in Fig. 12. A small bar through the head of the 
screw gives ample leverage for setting the screws tight, which 
is a matter of no small importance. The rod when extended 



32 



TOPOGRAPHIC STADIA SURVEYING 



i 



t 



J 



« 



i 

B 

§ 

V 



Fig. 14. — Stadia rod. 



-* B 

Fig. 15. — Two types of rod. A. For 
ordinary use. B. For long v sights. 



TOPOGRAPHIC STADIA SURVEYING 33 

should have no lost motion at the central joint. Thumb- 
screws of the type described, cut from about | in. iron, will 
stand much rough handling. 

When folded up the stiffening board is shifted to near the 
end of the rod, Fig. 13, where there are holes for the free 
passage of the thumb-screws through one leaf of the folded 
rod into the threaded holes of two more small iron plates set 
in the opposing face of the other leaf. The thumb-screws 
here not only hold the stiffening board securely in place, but 
clamp the two leaves of the rod, so that there can be no sliding 
of face against face. In its folded condition the rod is excep- 
tionally well protected and will stand much handling without 
injury. 

The preferred length has always been 11 or 12 ft. but 
shorter or longer rods may be found 
convenient. The folded length is just 
one-half of the full rod length. The 
top and bottom of the rod should be 
shod with strips of iron, though in 
the case of the top, lighter iron than 

in the case of the bottom may be Fig. 16. A two-tenth 

used, rod increment. 

The width of the rod should be at 
least 3J in. It may, at pleasure and to advantage, be made 
somewhat wider. 

Any type of lettering and subdivision may now be used, 
but one which is not likely ever to be abandoned if once 
tried, particularly by those who delight in using home-made 
rods, is the one shown in Figs. 14, 15, and 16. When the rod 
is wider than 3f ins. the spaces marked f in. Fig. 16, should be 
increased somewhat. A longer oblique line than shown, for 
the interpolation of hundredths of a foot, will be found 
advantageous. 

The reading is to the nearest hundredth of a foot along the 
oblique lines of the black triangle. The figures cut by the 
cross-hair are always read; they stand on the footmarks. 



• 3?+"- — 4 

1 



34 TOPOGRAPHIC STADIA SURVEYING 

The black rectangle of the odd tenths backed by a black 
triangle, together with the superimposed triangle of the next 
even tenth make a characteristic design, Fig. 16, which 
helps the eye to mount from point to point with certainty 
by two-tenth intervals. The tops of the figures are always 
three-tenths points. The five-tenth points are indicated 
by red diamond-shaped marks and the full foot by similar 
elongated red spear-heads, or half spear-heads, extending 
across the face of the rod. 

With telescopes of the ordinary power a rod of this kind 
with 3 J in. face is good for all distances ordinarily entering 
into stadia work. When sights exceeding 600 ft. are fre- 
quent, it will be found convenient to use a rod with the sub- 
divisions of the feet alternately at the left and at the right 
edge of the rod, as shown in Fig. 15. 

Any sign painter can paint such a rod. It can be marked 
in a few minutes. On the white painted surface, after 
drawing the longitudinal line at the base of the triangles, the 
foot marks are to be laid off with care, using a tested steel 
tape. That the foot marks should be correct is of prime 
importance. The zero point of the rod should preferably 
be at the top edge of the metal shoe, not at its bottom, which 
is subject to wear. Using a pattern cut from a sheet of tin 
or other convenient material, one foot long, the oblique 
limiting lines of all the black triangles can be drawn prac- 
tically with a continuous stroke. A stencil may be used in 
outlining the figures. The red diamonds may now be 
painted, then all the black on the rod. Sharp outlines of 
the markings can be secured by using a ruling pen before 
filling in with the brush. 

The red diamonds are convenient identification points for 
short sights. Colors can not be distinguished at long dis- 
tances, except when light is very favorable.* 

* A stadia rod in substantial agreement with the foregoing speci- 
fications has been put on the market by the A. Lietz Co., Instrument 
Manufacturers, San Francisco, Cal. 



TOPOGRAPHIC STADIA SURVEYING 



35 




■ tB*" 



For work requiring very long sights crosspieces at several 
points of the rod, projecting beyond its sides, and a slender 
extension with similar crosspieces, have 
repeatedly been found to be of great 
help. 

The wood used for such a rod should 
be straight-grain and well seasoned. 
According to the character of the wood 
chosen, the thickness of the rod and of 
the stiffening board may range from 
about f in. to | in. 

When the meter is the distance unit 
instead of the foot, the markings on the 
rod should be as shown in Fig. 17. Here 
again the eye recognizes at a glance the 
even and odd subdivisions. The readings 
can be made to the nearest tenth of a 
meter. Such a rod is serviceable for pre- 
cise leveling. 

The Elimination of the Height of the 
Telescope above the Instrument Sta- 
tion Plug. The ordinary method of 
doing stadia work requires that sights 
be taken for vertical angles to some point 
on the rod determined by the height i of 
the telescope above the station plug. It 
will be found much more convenient to 
disregard the height of the telescope 
above the instrument point altogether,* 
and to take all sights to the 5-ft. mark or jr IG 17 _a etric 
to some other selected foot mark which is stadia rod. 

at about the ordinary height of the tele- 
scope above the ground. That this height need not be the 
exact height of the telescope above the ground can readily 
be seen and will be better understood by reference to the 
* Dr. W. Jordan: Vermessungskunde, p. 630. 



36 TOPOGRAPHIC STADIA SURVEYING 

diagram Fig. 18. The difference in elevation between the 
point B in this diagram and the point C is entirely inde- 
pendent of the height of the tripod at the point A. It can 
be calculated from the two sights AB' and AC . The height 
of the telescope at A above the ground or above a plug does 
not have to be known at all, unless the elevation of the 
ground or of the plug at that point is to be determined. 

When it happens that the 5-ft. mark is not visible, the cross- 
hair may be set on some other foot mark, making note 
thereof, and proper attention must be paid to this fact when 
elevations are calculated. 

As the 5-ft. increment of the rod is neither added nor sub- 



"* "— < '^ V) 

Fig. IS. 

tracted in note-keeping it follows that all instrument station 
heights may be entered as ground heights, but that they are 
in fact fictitious. They are not the real instrument heights 
nor the exact ground heights at the instrument station, but 
are elevations 5 ft. lower than the actual height of the instru- 
ment. It is just the same as though the sights were along 
the dotted lines A'B and A'C, Fig. 18. 

In using this method of surveying it is desirable to begin 
as in ordinary leveling by letting the rod be held at the 
starting point. It will be found a convenience, and the 
chance of error in platting will be reduced, if backsights are 
entered in the notes as though they were sights taken from 
the rod to the instrument. 



TOPOGRAPHIC STADIA SURVEYING 37 

The Liberal Use of the Magnetic Needle. Before pre- 
senting a sample page of notes it may be well to explain the 
method of topographic stadia surveying which led to the 
foregoing simplification. In difficult country it is often 
found impracticable to select instrument stations in advance 
and it is frequently embarrassing to be compelled to occupy 
stations selected by assistants. The operations of setting 
up and of orientation consume valuable time. To eliminate 
these disadvantages of the ordinary method of work — it 
being, of course, assumed that the necessary triangulation 
work, base-line surveying and precise leveling to establish 
reference points has been done — a start may be made at any 
point of known position and elevation. 

The starting point may be called station zero. The rod is 
held at this point and the instrument is carried to the place 
from which sights can be taken to best advantage both with 
a view to getting the topography within reach and to making 
progress ahead. 

The azimuth is now determined by magnetic needle. 
Unless, for some reason, the instrument point is to be pre- 
served it need not be marked by a plug, neither is it necessary 
to determine the ground height at the instrument unless 
required by topographic considerations. The instrument 
station thus occupied is Station 1. The next turning point 
located by needle bearing, by stadia reading and by vertical 
angle is Station 2. The instrument is not set up at Station 2, 
but is carried on to Station 3, which is again selected with a 
view to comprehensive work. The position of Station 3 is 
fixed by direction and distance from 2, and so on. Back- 
sights for azimuth must, of course, be taken with reversed 
telescope, or the south end of the magnetic needle must be 
read. Care must also be taken to give the vertical angle 
its proper sign. It will be noted that the line becomes a 
continuous traverse line, the odd-numbered stations being 
instrument stations, the others turning points. 

For ground heights and short sights reliance may be had 



38 TOPOGRAPHIC STADIA SURVEYING 

upon the small levels attached to the plate of the transit 
and perhaps in some cases to the horizontal position of the 
plane table. For each foresight and for each backsight the 
vertical circle should be set at zero; the telescope is then 
pointed toward the rod, the tripod head screws, in the case 
of a transit, are used to bring the telescope level and then 
the sight is taken. The accuracy with which such work can 
be done with a transit and the areas that can be covered are 
surprising. The author has often had two to three rodmen 
at work and has found no trouble in the office interpretation 
of the field notes. 

The method of occupying with the instrument only the 
alternate or primary stations is particularly applicable in 
making surveys of reservoir and dam sites, in taking general 
topography over large areas and in securing data for topo- 
graphic maps of mining ground. 

The foregoing notes relating to the use of the magnetic 
needle in topographic surveying were written with special 
reference to surveys made with a transit. They are with 
slight modification of the text applicable also to plane-table 
map work. 

It remains to be said that a magnetic needle 5 ins. long 
should enable the field work to be done with about the same 
degree of accuracy at which the data can be platted on 
a scale of about 200 ft. to the inch ( 25 1 o ). Longer needles 
or other methods of work should be used when maps on a 
very large scale are required and a very high degree of accuracy 
is demanded. 

Stadia Notes. It has already been stated that the height 
at the instrument station, as carried into the notes, if the 
5-ft. mark be selected as an arbitrary sighting-point, is a 
fictitious height 5 ft. lower than the actual height of the 
instrument. It often happens that many sights can be 
taken without noting the vertical angle by using the transit 
as a level. In all such cases the level foresight as made 
should be recorded, but this rod-reading should not be 



TOPOGRAPHIC STADIA SURVEYING 39 

applied to the fictitous station height used in calculating 
elevations by vertical angle, but to the real height of the 
instrument. It will, therefore, be found convenient to insert 
in a a height of instrument " column the actual height of 
the instrument (the fictitious station height plus 5 ft.), sub- 
tracting from this, as in leveling, whenever the transit is 
used as a level. 

The fictitious transit station elevation, it will be noted, 
is carried forward into the column for ground heights and is 
identified by underlining. To this transit station elevation 
all differences in elevation, as determined by vertical angles 
with sights to the 5-ft. mark, are applied to calculate the 
ground heights. 

When, in taking a foresight or a sight to any point whose 
elevation is to be determined, the cross-hair in determining 
the vertical angle is set on some foot mark n other than the 
foot mark 5, then subtract (n — 5) from the elevation. 

When a backsight is taken to any mark n on the rod other 
than the foot mark 5 then add to the new instrument station 
height (n— 5) ft. 

The backsight which appears in the notes as though taken 
from an even numbered (secondary) station is, in fact, the 
first sight taken from the next instrument station. The 
notes thus become a simple combination of transit and level 
notes. 



40 



TOPOGRAPHIC STADIA SURVEYING 



NOTE-BOOK- 



LEFT-HAND PAGE 



Rod 
Read- 
ing. 


Dis- 
tance 


Magnetic 
Course. 


Vertical 
Angle. 


Difference in 
Elevation. 


Back- 
sight. 


Height 
of In- 
stru- 
ment. 


Level 
Sights, 
Fore- 
sight. 


362 

256 


Topog 

342 

257 
117 
372 
603 

288 
831 
883 
428 
717 

437 

926 
707 

331 


raphic Su 
The Eagl 

Station 

N27 15E 

Station 

S31 35W 
S80 30W 
S83 25W 
N45 OOW 
N36 10W 
N3 15E 
N20 30E 
N85 OOE 
N60 10E 

Station 
N40 15E 

Station 

S6 45E 
N35 05E 

Station 

N62 30E 


rvey of 
e Mine 
Oct. 17, 



+ 13.21 

1 

-2.52 
-3.17 
+2.00 

+8.14 
+ 12.05 
+ 16.09 
+ 15.30 

+2.17 
+8.07 

2 


1915 

+81.61 

-12.8 

-6.7 

+ 13.0 

+87.0 

+61.7 

+240.8 

-2.0+245.0 

+3.0+17.1 

+ 102.23 






116 








371 








613 








300 








900 








950 








428 








730 








436 


6.17 
327 . 43 


327.43 






3 












925 




8.3 


706 










3.16 


338 


4 

+9.11 


+53.48 

















TOPOGRAPHIC STADIA SURVEYING 41 



SAMPLE PAGES 



RIGHT-HAND PAGE 



Remarks. 



Transit No. 36. 
em 1.15 ft. 

All vertical angle sights are to the 5-ft. mark on the rod unless 
otherwise noted. 

Odd-numbered points are the instrument stations. 

Even-numbered points are the turning points. 
U. S. G. S. Bench, top of iron pipe, located, etc. 

To Station 1 gentle slope to S. 



Bottom of gulch. 
Slope to SW. 
Bottom of gulch. 
Bottom of gulch. 
Slope to W. 
Top of bluff. 
To 7 ft. Top of bluff. 
To 2 ft. Slope to S. 
To station 2. 



To Station 3. The fictitious (though approximate) elevation of 
ground at Station 3, and Station elevation is found by sub- 
tracting 5 ft. from the H. I. 



At E. edge of timber. 

To Station 4. Temporary B. M., etc. 



To Station 5. 



42 



TOPOGRAPHIC STADIA SURVEYING 



NOTE-BOOK— 



Rod 
Read- 
ing. 


Dis- 
tance. 


Magnetic 
Course. 


Vertical 
Angle. 


Difference in 
Elevation. 


Back- 
sight. 


Height 
of In- 
stru- 
ment. 


Level 
Sights, 
Fore- 
sight. 




511 


438 

461 

618 
417 

511 

538 


Station 
Nil 05W 


5 
-6.18 


-56.4 




382.75 




516 













5.2 


437 


N36 10W 

Station 
N20 00E 
Station 

N10 00E 
N51 20E 

Station 

N80 00E 

Station 

N31 45E 

Station 

Etc. 










9.26 


462 


6 
-3.56 

7 

+4.12 
-3.06 

8 A. 

+6.16 

8B. 

+ 12.56 

9 


+3-31.09 

+45.33 
-22.57 

+56.13 


• 






620 








417 
















516 














565 


+ 123.51 

















TOPOGRAPHIC STADIA SURVEYING 



43 



SAMPLE FACES— Continued 



Eleva- 
tions. 


Remarks. 


377.75 




321.4 




377.6 


Ground at instrument. 


373.49 


To Station 6. 


373.49 




344.80 


To 8 ft. to Station 7. 


390.13 


To Station 8A. 


322.23 


To Station 8B. 


390.13 




446.26 


To Station 9 


322.23 




445.74 


To Station 9 


446.00 




Etc. 





44 TOPOGRAPHIC STADIA SURVEYING 

Vertical Angles Measured with an Alidade. In using 
the alidade of the plane-table for measuring angles in a 
vertical plane, two readings on the vertical circle are neces- 
sary. First, the index error when the telescope, pointed 
toward the rod, is in a horizontal position; second, the 
angle when the telescope is depressed or elevated toward 
the sighting-point. A combination of the two readings 
gives the angle of depression or elevation. It would be a 
convenience to have the index arranged movable and pro- 
vided with a tangent screw, similar to the lower plate of the 
transit, so that the telescope could be leveled carrying 
with it the index set at zero. Unclamping and sighting 
could then be followed, as with a transit, by a reading of 
the vertical angle freed from index error. The index error 
here referred to is due to the fact that a plane-table is not 
expected to have a perfectly true surface and cannot be 
leveled with the accuracy desirable in measuring vertical 
angles. 

The Amount of Error when the Sighting Point does not 
Bisect the Intercept. The formulas presented in this manual 
are based on the assumption that the portion of the stadia rod 
which is read for distance is bisected by the middle cross-hair 
when the vertical angle is read. As a matter of fact this 
condition rarely obtains in practice. The lower cross-hair 
is set upon some foot mark and the intercept is read on the 
upper cross-hair, thereupon the middle cross-hair is set upon 
the sighting-point and the rodman is waved off. 

In order that the topographer may have a clear concep- 
tion of the error introduced when the rod is read for distance 
with the middle cross-hair at some point on the rod other 
than the sighting-point, Tables 1 and 2 have been prepared. 
It will be seen from these that for small vertical angles and 
sights of any length, very little attention need be paid to the 
portion of the rod used in measuring distance. The impor- 
tance of having the middle cross-hair near the sighting-point 
when reading for distance, increases, regardless of the actual 



TOPOGRAPHIC STADIA SURVEYING 



45 



distance to the rod, as the angle of elevation or depression 
increases. 

Table 1 

TABLE OF CORRECTIONS TO BE APPLIED WHEN THE 
ROD IS READ WITH THE TELESCOPE AT A VERTICAL 
ANGLE OF GREATER AMPLITUDE THAN THE RE- 
CORDED VERTICAL ANGLE (TO THE SIGHTING- 
POINT). DECREASE THE DISTANCE AND DECREASE 
THE DIFFERENCE IN ELEVATION BY THE AMOUNTS 
NOTED IN THE TABLE 





0> .J 

.S3 o+r 

g3M 


Vert. 


Angle 


Vert. 


Angle 


Vert. Angle 


Vert. Angle 


Vert. Angle 




= 


1° 


= 


5° 


= 10° 


= 20° 


= 30° 


M 

3 


Corrections 


Corr? 


ctions 


Corrections 


Corrections 


Corrections 


eU 


§%* 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


& 


:2Qa3 
















TJ 






















& 


§ 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


100 


1 


.04 





.18 


.02 


.34 


.06 


.66 


.24 


.86 


.50' 


100 


2 


.13 





.41 


.04 


.70 


.13 


1.32 


.48 


1.72 


1.00 


100 


3 


.23 





.64 


.06 


1.07 


.20 


1.98 


.73 


2.58 


1.50 


100 


4 


.32 





.87 


.08 


1.44 


.27 


2.65 


.97 


3.45 


2.00 


100 


5 


.42 





1.11 


.10 


1.91 


.34 


3.32 


1.21 


4.32 


2.50 


200 


1 


.04 





.2 


.02 


.3 


.05 


.6 


.20 


.9 


.50 


200 


2 


.10 





.4 


.03 


.7 


.12 


1.3 


.45 


1.7 


1.00 


200 


3 


.17 





.6 


.05 


1.1 


.18 


1.9 


.70 


2.6 


1.50 


200 


4 


.23 





.8 


.07 


1.5 


.25 


2.6 


.95 


3.5 


2.00 


200 


5 


.30 





1.0 


.09 


1.9 


.32 


3.3 


1.20 


4.3 


2.50 


500 


1 


.04 





.2 


.02 


.3 


.05 


.6 


.23 


.9 


.45 


500 


2 


.08 





.3 


.03 


.7 


.11 


1.2 


.46 


1.7 


.95 


500 


3 


.13 





.5 


.05 


1.1 


.17 


1.9 


.70 


2.6 


1.45 


500 


4 


.18 





.7 


.06 


1.5 


.23 


2.5 


.93 


3.4 


1.95 


500 


5 


.23 





.9 


.08 


1.8 


.30 


3.2 


1.16 


4.3 


2.45 


1000 


1 


.03 





.2 


.02 


.4 


.06 


.7 


.23 


.9 


.45 


1000 


2 


.07 





.3 


.03 


.7 


.12 


1.3 


.46 


1.7 


.95 


1000 


3 


.11 





.5 


.05 


1.0 


.18 


1.9 


.70 


2.6 


1.40 


1000 


4 


.15 





.7 


.06 


1.3 


.24 


2.6 


.93 


3.4 


1.90 


1000 


5 


.20 





.9 


.08 


1.7 


.30 


3.2 


1.16 


4.3 


2.40 



The tables are prepared as correction tables, but it will be 
well to remember that no correction is necessary if the rule 
be observed requiring the middle cross-hair to be first placed 
on the sighting-point, and then setting the lower cross-hair 



46 



TOPOGRAPHIC STADIA SURVEYING 



upon the foot mark nearest to the lowest cross-hair. The 
error under observance of this rule will be so small as to be 
negligible in all surveys, except in special cases where the 
highest attainable accuracy may be a requirement. 

Whenever the bisecting point of the intercept is within 
one foot of the sighting-point the error in distance for any 
vertical angle less than 30° cannot exceed 1 ft. 



Table 2 

TABLE OF CORRECTIONS TO BE APPLIED WHEN THE 
ROD IS READ WITH THE TELESCOPE AS A VERTICAL 
ANGLE OF LESS AMPLITUDE THAN THE RECORDED 
VERTICAL ANGLE (TO THE SIGHTING-POINT). IN- 
CREASE THE DISTANCE AND INCREASE THE DIF- 
FERENCE IN ELEVATION BY THE AMOUNTS NOTED 
IN THE TABLE 





81* 


Vert. Anglo 


Vert. 


Anglo 


Vert. Angle 


Vert. Angle 


Vert. Angle 




= 1° 


= 


5° 


= 10° 


= 20° 


= 30° 




m tn O 
E 9 be 














a 
•9 


Corrections 


Corrections 


Corrections 


Corrections 


Corrections 


Cj 


<->§.g 


Feet. 


Feet. 


Feet. 


Feet. 


Feet. 


& 


-COM 

20k 














Ti 






















& 


§ 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


100 


1 


.02 





.16 


.01 


.33 


.05 


.63 


.22 


.87 


.50 


100 


2 


.03 





.31 


.03 


.64 


.10 


1.25 


.44 


1.73 


1.00 


100 


3 


.02 





.44 


.04 


.94 


.16 


1.85 


.66 


2.59 


1.50 


100 


4 


-.02 





.54 


.05 


1.22 


.21 


2.44 


.88 


3.46 


1.95 


100 


5 


-.08 





.62 


.05 


1.49 


.26 


3.07 


1.10 


4.32 


2.40 


200 


1 


.03 





.2 


.01 


.3 


.06 


.6 


.22 


.9 


.50 


200 


2 


.05 





.3 


.03 


.7 


.12 


1.2 


.45 


1.7 


1.00 


200 


3 


.06 





.5 


.04 


1.0 


.17 


1.9 


.67 


2.6 


1.50 


200 


4 


.06 





.6 


.05 


1.3 


.23 


2.6 


.89 


3.4 


1.95 


200 


5 


.05 





.7 


.06 


1.6 


.28 


3.2 


1.12 


4.3 


2.40 


500 


1 


.03 





.2 


.01 


.3 


.06 


.6 


.23 


.9 


.50 


500 


2 


.05 





.3 


.03 


.7 


.12 


1.2 


.46 


1.7 


1.00 


500 


3 


.07 





.5 


.04 


1.0 


.17 


1.9 


.68 


2.6 


1.50 


500 


4 


.09 





.7 


.06 


1.3 


.23 


2.6 


.91 


3.4 


1.95 


500 


5 


.10 





.8 


.07 


1.6 


.28 


3.2 


1.14 


4.3 


2.40 


1000 


1 


.03 





.2 


.01 


.4 


.06 


.6 


.23 


.9 


.50 


1000 


2 


.06 





.3 


.03 


.7 


.12 


1.3 


.46 


1.7 


1.00 


1000 


3 


.09 





.5 


.04 


1.1 


.18 


1.9 


.70 


2.6 


1.50 


1000 


4 


.12 





.7 


.06 


1.4 


.24 


2.6 


.93 


3.4 


1.95 


1000 


5 


.15 





.8 


.07 


1.7 


.30 


3.2 


1.16 


4.3 


2.40 



TOPOGRAPHIC STADIA SURVEYING 47 

The columns in the tables bearing the heading " Middle 
hair departures from the sighting-point " contain the depart- 
ure of the bisecting point of the intercept from the sighting- 
point for which the corrections in the succeeding columns 
have been computed. 

The sighting can, as stated, always be done in such manner 
that the use of these tables will not be necessary. Their 
introduction is mainly for the purpose of showing the errors 
that will result if proper attention be not paid to the part 
of the rod read for distance. 

Amount of Error Due to Inclined Rod. If the stadia 
rod be not held in a true vertical position, or if, in the case 
of a sectional rod the face of the rod is in two or more planes, 
appreciable error may result. All such error should be 
avoided. Nevertheless in order that the magnitude thereof 
may not be underestimated attention is called to the following 
facts. 

Let it be supposed that a rod is built up of two sections of 
which the uppermost is fastened to the back of the lower one 
and that the thickness of the lower section and, therefore, 
the departure of the upper section from the plane of the lower 
one is J of an inch or .0875 ft. 

If now a reading for distance is made on this rod with one 
cross-hair on the lower and one on the upper section the 
resulting error in distance will be : 

For vertical angle + 5° rod reading too small by 0.8 ft. 
For vertical angle +10° rod reading too small by 1.5 ft. 
For vertical angle +20° rod reading too small by 3.2 ft. 
For vertical angle +30° rod reading too small by 5.0 ft. 
For vertical angle — 5° rod reading too large by 0.8 ft. 
For vertical angle —10° rod reading too large by 1.5 ft. 
For vertical angle -20° rod reading too large by 3.2 ft. 
For vertical angle —30° rod reading too large by 5.0 ft. 

It is to be noted that in the case of short sights the per- 
centage of error when sighting up or down will be relatively 



48 TOPOGRAPHIC STADIA SURVEYING 

high. The amount of this error is independent of the dis- 
tance, being dependent solely upon the vertical angle of the 
sight and the departure of the surface on which one cross- 
hair is read from that on which the other is read. 

When due to carelessness or any other cause the stadia 
rod is inclined forward or backward, and departs from a 
true vertical plane, the error will be as shown in Tables 3 
and 4. 

The Accuracy of Telemeter Surveys. The accuracy 
of the survey made with the telemeter and stadia rod is not 
readily determinable. The error in single readings may 
vary within considerable limits. The reading is affected 
not alone by the care with which the telemeter and the rod 
have been constructed, but also by atmospheric and light 
conditions and by the personal equation of the observer. 

Under fair conditions the individual readings, when the 
distances do not exceed 800 ft. should have a probable error 
less than 1 in 500. When a survey is under consideration 
made up of a number of courses, aggregating about a mile 
in length, the error with ordinary care and with instruments 
suitable for ordinary good work, should not exceed 1 in 
1000. When a still longer distance is measured by many 
sights, each less than 800 ft., the probable error will be less 
than this amount. According to the law of least squares, 
possibly 1 in 2000 when the aggregate length of the survey is 
about 4 miles. 

In view of the relatively large possible error in a single 
sight, it would be useless to note distances other than to 
the nearest foot, when ordinary topographic surveys are 
involved. Elevations of temporary reference points, such 
as turning-points and of permanent bench marks, should be 
entered in the notes to hundredths. The height of instru- 
ment, too, should be entered to hundredths of a foot. The 
elevation of the ground at any point and the differences in 
elevation for use in determining ground heights should be 
noted to tenths only. 



TOPOGRAPHIC STADIA SURVEYING 



o .S-o 

E feOO 

W7 •=! rt 



o 

o 
H 

> 



* 2 



T3J3 
ft >> 



o 

Q 
O 



co 



9§ 

w 

a 

H 

O 

CQ 

a 
p 

H 

Ph 

5 

« 
o 

O 

5 
O 
W 

S 

o 
o 






j-8 

o lia 






2 S o 

■^03 

-^ fl _. 

n " 2 

d a 
,d o-*> 



.2 353 

o £ > 
••« d 

d d^ 
i« 

a *H 





Q 


^ 


<NtNJ<N xtfT*^ OJOSOS iCiOuo 

QO0000 OOO »OiO»0 000000 COCOCO 

1-lT-tr-t COCOCO T*1T^rt< t^t^t> —I.-!,-! 




£ 


- i . 8? 

- 9.10 

- 18.2 

- 3.04 

- 15.2 

- 30.4 

- 4.59 
-22.9 

- 45.9 

- 7.85 

- 39.2 

- 78.5 

- 11.6 

- 57.8 
-115.6 


-J 
51 

B 

M 

m 

> 


iQ 


^ 


.53 
.53 
.53 

1.14 
1.14 
1.14 

1.92 
1.92 
1.92 

3.55 
3.55 
3.55 

5.41 
5.41 
5.41 


& 


COiO<N Tt<ia CO<M rf o 

tO COCO i-H>Tf< 03CO<N lOOOia <*#*«H 

<N lO i-tiOi-H 1-H0505 C0t>»O lOt^Tjl 
H i-l HCO <N»0 

III III III III III 


K 
H 

3 
o 
p 


co 


£ 


.23 
.23 
.23 

.59 
.59 
.59 

1.06 
1.06 
1.06 

2.04 
2.04 
2.04 

3.15 
3.15 
3.15 


S 
Eh 


£ 


co-^oo a5t>."* coos ^t~ io 

(NrHcN 10050) 0<NiO Oi-f-* i-H00»O 
--i(N <NO HiflO MOO C0iO.-t 

iii iii i m iT i i77 


o 
■ 




o 




^ 


<N<N<N COCOCO l^t»t>- COCOCO t>. r>- h- 
i-IfH.-I COCOCO COCOCO COCOCO ooo 

i-t fH r-t <N (N 1 <N 


to 

< 




- .12 

- .60 

- 1.21 

- .36 

- 1.83 

- 3.65 

- .67 

- 3.37 

- 6.75 

- 1.33 

- 6.63 
-13.3 

- 2.07 
-10.3 
-20.7 




& 


^'•^tJ* t^f~t>. (NINO* lO»OiO <N(N<N 
OOO i-Hr-lrH COCOCO CO CO CO OOO 

i-tr-<i-l 




£ 


- .04 

- .23 

- .45 

- .17 

- .84 

- 1.67 

- .32 

- 1.60 

- 3.22 

- .65 

- 3.24 

- 6.4S 

- 1.02 

- 5.10 
-10.2 


Rod 

Reading. 

Ft. 


100 

500 

1000 

100 

500 

1000 

100 

500 

1000 

100 

500 

1000 

100 

500 

1000 




1j 

IP 


i 

X 

3 


O o o o 

i-* iO O O O 
«-• <M CO 



+» M 



50 



TOPOGRAPHIC STADIA SURVEYING 



o 

H 
go 
O 
Ph 

»J 

<J 
o 

H 

F 

w 
p 

H 



33 

GQ C 

£ o 
O o) 



.S.9 



a n 



93 ,2o 

g 18 

8tSH 

^ 3 © b 

M ** rt 

O c^ o 



p 

H 

< 

PL. 
W 

Q 

« 

c 

Ph 

o 

p 

o 
w 

rt 
o 
o 



* fl I 

a o m 



0) m .rt 
O fl <D 

13s*. 









J 

<! 
O 
H 

« 
W 

H 

a 

Eh 

SI 
o 

M 

K 
w 
M 
p 

M 

& 
H 
P 

h 
O 

H 

O 


© 

o 


6? 


CNCNtN 


ooo 


lOiOiO 


00 00 00 


CO CO CO 
lOiOiO 

00 00 00 


H-> 


NON 

OJHH 

HCOCN 

i 1 7 


ooo 


Hl>lO 


00Oh 
•tf <*00 


CO 

iCCOfN 

00 (N iO 

Tt<00 


£ 


CO CO CO 


00 00 00 
CO CO CO 


322 




co co co 






HHH 


CNCNCN 


^T* 


H-> 


COlO© 
CNHCO 


00OO 
COO5 00 


<HH(N 
Ht>-«H 


t^oot> 


5* 

COHCO 


1 1 1 


HCO 


HUJH 


c*cor>- 

HCN 


Tj- COCO 
CN-* 


o 

CO 


t>° 


ooo 


CO CO CO 


00 00 00 


co CO CO 


00 00 00 








T-HHH 


(MCMCM 


£ 


lOCOCO 
0(NrJi 


i-hOO 
COCOtN 


lOHCO 
lOCiO 


COO 

t^oot^ 


00^t^ 


1 1 1 


T-HCO 


cot^ 


T-H00CO 


(NTfOO 
hCt 


CI 


S* 


OOO 


<N(N<N 


lOiOiO 


<M<N(N 


lOiOO 






HHH 


, ~ ,THrH 


£ 


ooo 


T*<HCO 

<MCM ■* 


>oio co 


CM OH 


lOCO 
OMO 


HCN 


(NO 


HCDcN 


HffiO 


- 


^ 


ooo 


CO CO CO 


ooo 

CO CO CO 


CO CO CD 


go. 




£ 


(NOOiO 
OOH 


cooot^ 

t-HCO CO 


o>cN 

CO-tfCi 


H00 00 

©OH 


oooo 




■" 


h<N 


coo 


"*Oi 




b 


3 


ooo 

ooo 

HlOO 


ooo 
ooo 

HLOO 


ooo 

ooo 

HlOO 


ooo 

ooo 

HlOO 


ooo 
ooo 

HlOO 




1i 

C c 


1 


H 


o 




o 

H 


o 

O 


o 

CO 



TOPOGRAPHIC STADIA SURVEYING 51 

The Effect of Refraction. As is well known the refraction 
of light rays is a function of the unequal density of the 
atmosphere. Near the ground surface, at times when there 
is material difference in the temperature of the air and of the 
ground, there may be a material variation in the refraction 
with but a few feet difference in the elevation of the light 
ray. The refraction will in other words be different for the 
light rays from the lower and upper portions of a telemeter 
rod. This fact and its influence upon the measurement of 
distances by means of a telescope and stadia rod has been 
ably 'discussed by Mr. L. S. Smith, C. E.,* and need not be 
dwelt upon here. It will suffice to say that the refraction 
effect Upon the rod-readings is greatest at midday and is not 
the same on different days. The rating and testing of the 
telemeter should, therefore, be extended over a number of 
days and should include observations in the morning and 
evening as well as at midday. 

Instances have been found where, in dry, arid regions such 
as Arizona, the errors due to refraction have been so great 
that the use of the ordinary stadia rod has had to be aban- 
doned for accurate work. In such instances, the use of a 
horizontal rod with a special supporting device can be rec- 
ommended. 

* University of Wisconsin Bulletin, Engineering Series, Vol. 1, 
No. 5. 



CHAPTER VII 
THE PLATTING OF STADIA NOTES 

When topographic surveys are made with a transit the 
field observations — except foresights and backsights — are 
usually reduced in the office, where, too, the notes are platted. 

In order that the work may readily be manifolded the aim 
is to secure an inked copy on tracing linen or other trans- 
parent material with the least degree of labor. 

The following procedure can be recommended: 

Use an open protractor of thin material, such as paper, 
with radius equal to or greater than the lengths of the sights 
to be platted. Make the pencil drawing upon the rough side 
of tracing linen or upon tracing paper placed over cross-section 
or profile paper. The closely spaced parallel lines visible 
through the tracing linen are an invaluable aid in the quick 
orientation of the protractor whenever the azimuths are 
referred to the north line or whenever they are given in the 
relation to the cardinal points of the compass. 

By placing a scale, or a marked ruler, or a strip of paper, 
north and south or east and west across the protractor, the 
same can be conveniently centered and oriented at one 
operation. No lines from instrument station to topographic 
points should be drawn. The only survey lines to appear on 
the drawing are those of the traverse from station to station. 
A fine needle at the instrument station from which the sights 
are being platted is a convenience and will decrease the lia- 
bility of making errors in platting. Special scales with zero 
point swinging upon this needle and other devices to simplify 
the office work readily suggest themselves. 

52 



TOPOGRAPHIC STADIA SURVEYING 53 

After the pencil drawing has been made and corrected to 
fit the controlling points of the survey, a fresh sheet of 
tracing linen is used upon which to ink the finished map. 
This is then available for any of the ordinary processes of 
manifolding, such as blue or black printing, photolithograph- 
ing, etc. 



CHAPTER VIII 
TABLES 

A number of tables are here presented which the sur- 
veyor who uses his transit as a telemeter or who makes 
topographic surveys with the plane table will find useful. 

Table 5 gives the values of the terms e cos a. and e sin a 
which appear in the correct stadia formulas (17) and (18) 
and covers all ordinary values of e. For each instrument, 
there being but one value of e, only a single line of the table 
will apply. This particular line should be made the basis 
of a secondary table for the topographer's own instrument, 
giving the values for each degree so that interpolation will be 
simplified. 

Table 5 

VALUES OF e cos « AND e sin a FOR DIFFERENT VALUES 
OF INSTRUMENT CONSTANT e AND DIFFERENT 
ANGLES OF ELEVATION a 

All values in feet 



Values 


1° 


5° 


10° 


15° 


20° 


30° , 


of e 


e cos 


e sin 


e cos 


e sin 


e cos 


e sin 


e cos 


e sin 


e cos 


e sin 


e cos 


e sin 


0.80 
1.00 
1.20 
1.40 
1.60 
1.80 
2.00 
2.50 


0.80 
1.00 
1.20 
1.40 
1.60 
1.80 
2.00 
2.50 


.01 
.02 
.02 
.03 
.03 
.03 
.03 
.04 


.80 
1.00 
1.19 
1.39 
1.59 
1.79 
1.99 
2.49 




07 
09 
10 

12 
11 
16 
17 
22 


.79 
.98 
1.18 
1.38 
1.57 
1.77 
1.97 
2.46 


.14 
.17 
.21 
.24 
.28 
.31 
.35 
.43 


.77 
.97 
1.16 
1.35 
1.54 
1.74 
1.93 
2.41 


.21 
.26 
.31 
.36 
.41 
.47 
.52 
.65 


.75 

.94 

1.13 

1.32 
1.50 
1.69 
1.88 
2.35 


.27 
.34 

.41 
.48 
.55 
.62 

.68 
.85 


.69 
.87 
1.04 
1.21 
1.39 
1.56 
1.73 
2.16 


.40 
.50 
.60 
.70 
.80 
.90 
1.00 
1.25 



54 



TOPOGRAPHIC STADIA SURVEYING 55 



STADIA REDUCTION TABLE 

Table 6 is a stadia reduction table, checked by Mr. Otto 
von Geldern, to facilitate the solution of the equations. 

D=r cos" <x+e cos «; .... (17) 

h=r sin a cos a+e sin a; . . .(18) 

or 

sin 2a . .,„ 

h=r — = \-e sin a (19) 

The tables as here published contain only the increments 
100 cos ? a and 100 sin a cos a. 

In using formulas (17) and (18) the values taken from the 

r 
tables are to be multiplied by r^r. In determining dis- 
tance e cos a and in determining difference in elevation 
e sin a are then to be added to the values found in the tables. 
In illustrating the use of these tables Mr. von Geldern uses 
the following figures : 

For a rod-reading r=285 ft. and a vertical angle 10° 12' 
there will be found in the table in the column " Hor. Dist." 
96.86 and in the column " Diff. Elev." 17.43; in other words 

100cos 2 (10°12 , )=96.86ft., 
and 

100 sin (10° 12 r ) cos (10° 12') =17.43 ft. 

285 
Both oHhese values are to be multiplied by j^ =2.85. 

Therefore 

285 cos 5 (10° 12') =2.85X96.86 =276.05; 

285 sin (10° 12') cos (10° 12') =2.85x17.43=49.67. 



56 TOPOGRAPHIC STADIA SURVEYING 

If a large ordinary transit has been used the value of e will 
be about 1.15 ft., and therefore 

1.15 cos (10° 12 r ) = 1.13; 
and 

1.15 sin (10° 12') =0.21, 
consequently 

D =276.05+1.13 =277.18; 

h =49.67 +0.21 =49.88. 

The chief value of Table 6 lies in the fact that it is applica- 
ble to the solution of the approximation formulas which are 
recommended in this manual for use in stadia surveying. 
Thus in the case of 

(27) D = (r+e) cos 2 «; 
and 

(28) h = (r +e) sin a cos a. 

For the special case (r+e) =285+1.15 =286.15; 

D «^jp X96.86 =277.16 ft.; 

286 1 5 
A=-^-Xl7.43=49.88ft. 

Again in the case of 

(29) D = (r+1) cos 2 a; 

(30) h = (r +1) sin a cos a. 

For the special case of (r+1) =286; 

286 
£=JqqX 96.86 =277.02 ft.; 

286 
&=—X 17.43 =49.85 ft. 



TOPOGRAPHIC STADIA SURVEYING 



57 



Table 6 
STADIA REDUCTION TABLE 

For instruments rated 1 to 100 

In the column " Hor. Dist." find: 100 cos 2 a 
In the column " Diff. Elev." find: 100 sin a cos < 
Rod Vertical 



Min. 


0° 


1 




2 




3 




4 


o 




Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 




Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 





100.00 


.00 


P9.97 


1.74 


99.88 


3.49 


99.73 


5.23 


99.51 


6.96 


2 


100.00 


.06 


09.97 


1.80 


99.87 


3.55 


99.72 


5.28 


99.51 


7.02 


4 


100.00 


.12 


£3.97 


1.86 


99.87 


3.60 


99.71 


5.34 


99.50 


7.07 


6 


100.00 


.17 


99.96 


1.92 


99.87 


3.6G 


99.71 


5.40 


99.49 


7.13 


8 


100.00 


• 23 


99.96 


1.98 


99.86 


3.72 


99.70 


5.46 


99.48 


7.19 


10 


100.00 


.29 


99.96 


2.04 


99.86 


3.78 


99.69 


5.52 


99.47 


7.25 


12 


100.00 


.35 


99.96 


2.09 


99.85 


3.84 


99.69 


5.57 


99.46 


7.30 


14 


100.00 


.41 


99.95 


2.15 


99.85 


3.90 


99.68 


5.63 


99.46 


7.36 


16 


100.00 


.47 


99.95 


2.21 


99.84 


3.95 


99.68 


5.69 


99.45 


7.42 


18 


100.00 


.52 


99.95 


2.27 


99.84 


4.01 


99.67 


5.75 


99.44 


7.48 


20 


100.00 


.58 


99.95 


2.33 


99.83 


4.07 


99.66 


5.80 


99.43 


7.53 


22 


100.00 


.64 


99.94 


2.38 


99.83 


4.13 


99.66 


5.86 


99.42 


7.59 


24 


100.00 


.70 


99.94 


2.44 


99.82 


4.18 


99.65 


5.92 


99.41 


7.65 


26 


99.99 


.76 


99.94 


2.50 


99.82 


4.24 


99.64 


5.98 


99.40 


7.71 


28 


99.99 


.81 


99.93 


2.56 


99.81 


4.30 


99.63 


6.04 


99.39 


7.76 


30 


99.99 


.87 


99.93 


2.62 


99.81 


4.36 


99.63 


6.09 


99.38 


7.82 


32 


•99.99 


.93 


99.93 


2.67 


99.80 


4.42 


99.62 


6.15 


99.38 


7.88 


34 


99.99 


.99 


99.93 


2.73 


99.80 


4.48 


99.62 


6.21 


99.37 


7.94 


36 


99.99 


1.05 


99.92 


2.79 


99.79 


4.53 


99.61 


6.27 


99.36 


7.99 


38 


99.99 


1.11 


99.92 


2.85 


99.79 


4.59 


99.60 


6.33 


99.35 


8.05 


40 


99.99 


1.16 


99.92 


2.91 


99.78 


4.65 


99.59 


6.38 


99.34 


8.11 


42 


99.98 


1.22 


99.91 


2.97 


99.78 


4.71 


99.59 


6.44 


99.33 


8.17 


44 


99.98 


1.28 


99.91 


3.02 


99.77 


4.76 


99.58 


6.50 


99.32 


8.22 


46 


99.98 


1.34 


99.90 


3.08 


99.77 


4.82 


99.57 


6.56 


99.31 


8.28 


48 


99.98 


1.40 


99.90 


3.14 


99.76 


4.88 


99.56 


6.61 


99.30 


8.34 


50 


99.98 


1.45 


99.90 


3.20 


99.76 


4.94 


99.56 


6.67 


99.29 


8.40 


52 


99.98 


1.51 


99.89 


3.26 


99.75 


4.99 


99.55 


6.73 


99.28 


8.45 


54 


99.98 


1.57 


99.89 


3.31 


99.74 


5.05 


99.54 


6.78 


99.27 


8.51 


56 


99.97 


1.63 


99.89 


3.37 


99.74 


5.11 


99.53 


6.84 


99.26 


8.57 


58 


99.97 


1.69 


39.88 


3.43 


99.73 


5.17 


99.52 


6.90 


99.25 


8.63 


60 


99.97 


1.74 99.88 


3.49 99.73 


5.23 


99.51 


6.96 


99.24 


8.68 



58 



TOPOGRAPHIC STADIA SURVEYING 



In the column 
In the column 



Table 6. — Continued 

STADIA REDUCTION TABLE 

For instruments rated 1 to 100 

Hor. Dist." find: 100 cos 2 a 
Diff. Elev." find: 100 sin a. cos a 
Rod Vertical 



Min. 


5 





6 


o 


7 


o 


8 


o 


9 


o 




Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 




Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 





99.24 


8.68 


98.91 


10.40 


98.51 


12.10 


98.06 


13.78 


97.55 


15.45 


2 


99.23 


8.74 


98.90 


10.45 


98.50 


12.15 


98.05 


13.84 


97.53 


15.51 


4 


99.22 


8.80 


98.88 


10.51 


98.48 


12.21 


98.03 


13.89 


97.52 


15.56 


6 


99.21 


8.85 


98.87 


10.57 


98.47 


12.26 


98.01 


13.95 


97.50 


15.62 


8 


99.20 


8.91 


98.86 


10.62 


98.46 


12.32 


98.00 


14.01 


97.48 


15.67 


10 


99.19 


8.97 


98.85 


10.68 


98.44 


12.38 


97.98 


14.06 


97.46 


15.73 


12 


99.18 


9.03 


98.83 


10.74 


98.43 


12.43 


97.97 


14.12 


97.44 


15.78 


14 


99.17 


9.08 


98.82 


10.79 


98.41 


12.49 


97.95 


14.17 


97.43 


15.84 


16 


99.16 


9.14 


98.81 


10.85 


98.40 


12.55 


97.93 


14.23 


97.41 


15.89 


18 


99.15 


9.20 


98.80 


10.91 


98.39 


12.60 


97.92 


14.28 


97.39 


15.95 


20 


99.14 


9.25 


98.78 


10.96 


98.37 


12.66 


97.90 


14.34 


97.37 


16.00 


20 


99.13 


9.31 


98.77 


11.02 


98.36 


12.72 


97.88 


14.40 


97.35 


16.06 


22 


99.11 


9.37 


98.76 


11.08 


98.34 


12.77 


97.87 


14.45 


97.33 


16.11 


24 


99.10 


9.43 


98.74 


11.13 


98.33 


12.83 


97.85 


14.51 


97.31 


16.17 


26 


99.09 


9.48 


98.73 


11.19 


98.31 


12.88 


97.83 


14.56 


97.29 


16.22 


28 


99.08 


9.54 


98.72 


11.25 


98.29 


12.94 


97.82 


14.62 


97.28 


16.28 


30 


99.07 


9.60 


98.71 


11.30 


98.28 


13.00 


97.80 


14.67 


97.26 


16.33 


32 


99.06 


9.65 


98.69 


11.36 


98.27 


13.05 


97.78 


14.73 


97.24 


16.39 


36 


99.05 


9.71 


98.68 


11.42 


98.25 


13.11 


97.76 


14.79 


97.22 


16.44 


38 


99.64 


9.77 


98.67 


11.47 


98.24 


13.17 


97.75 


14.84 


97.20 


16.50 


40 


99.03 


9.83 


98.65 


11.53 


98.22 


13.22 


97.73 


14.90 


97.18 


16.55 


42 


99.01 


9.88 


98.64 


11.59 


98.20 


13.28 


97.71 


14.95 


97.16 


16.61 


44 


99.00 


9.94 


98.63 


11.64 


98.19 


13.33 


97.69 


15.01 


97.14 


16.66 


46 


98.99 


10.00 


98.61 


11.70 


98.17 


13.39 


97.68 


15.06 


97.12 


16.72 


48 


98.98 


10.05 


98.60 


11.76 


98.16 


13.45 


97.66 


15.12 


97.10 


16.77 


50 


98.97 


10.11 


98.58 


11.81 


98.14 


13.50 


97.64 


15.17 


97.08 


16.83 


52 


98.96 


10.17 


98.57 


11.87 


98.13 


13.56 


97.62 


15.23 


97.06 


16.88 


54 


98.94 


10.22 


98.56 


11.93 


98.11 


13.61 


97.61 


15.28 


97.04 


16.94 


56 


98.93 


10.28 


98.54 


11.98 


98.10 


13.67 


97.59 


15.34 


97.02 


16.99 


58 


98.92 


10.34 


98.53 


12.04 


98.08 


13.73 


97.57 


15.40 


97.00 


17.05 


60 


98.91 


10.40 


98.51 


12.10 


98.06 


13.78 


97.55 


15.45 


96.98 


17.10 



TOPOGRAPHIC STADIA SURVEYING 



59 



Table 6. — Continued 

STADIA -REDUCTION; TABLE 

For instruments rated 1 to 100 
In the column " Hor. Dist." find: 100 cos 2 a 
In the column " Diff. Elev." find: 100 sin a cos a 
Rod Vertical 



Min. 


1C 


° 


11 


o 


li 


o 


13 




14 






Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 




Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 





96.98 


17.10 


96.36 


18.73 


95.68 


20.34 


94.94 


21.92 


94.15 


23.47 


2 


96.96 


17.16 


96.34 


18.78 


95.65 


20.39 


94.91 


21.97 


94.12 


23.52 


4 


96.94 


17.21 


96.32 


18.84 


95.63 


20.44 


94.89 


22.02 


94.09 


23.58 


6 


96.92 


17.26 


96.29 


18.89 


95.61 


20.50 


94.86 


22.08 


94.07 


23.63 


8 


96.90 


17.32 


96.27 


19.85 


95.58 


20.55 


94.84 


22.13 


94.04 


23.68 


10 


96.88 


17.37 


96.25 


19.00 


95.56 


20.60 


94.81 


22.18 


94.01 


23.73 


12 


96.86 


17.43 


96.23 


19.05 


95.53 


20.66 


94.79 


22.23 


93.98 


23.78 


14 


96.84 


17.48 


96.21 


19.11 


95.51 


20.71 


94.77 


22.28 


93.95 


23.83 


16 


96.82 


17.54 


96.18 


19.16 


95.49 


20.76 


94.73 


22.34 


93.93 


23.88 


18 


96.80 


17.59 


96.16 


19.21 


95.46 


20.81 


94.71 


22.39 


93.90 


23.93 


20 


96.78 


17.65 


96.14 


19.27 


95.44 


20.87 


94.68 


22.44 


93.87 


23.99 


22 


96.76 


17.70 


96.12 


19.32 


95.41 


20.92 


94.66 


22.49 


93.84 


24.04 


24 


96.74 


17.76 


96.09 


19.38 


95.39 


20.97 


94.63 


22.54 


93.81 


24.09 


26 


96.72 


17.81 


96.07 


19.43 


95.36 


21.03 


94.60 


22.60 


93.79 


24.14 


28 


96.70 


17.86 


96.05 


19.48 


95.34 


21.08 


94.58 


22.65 


93.76 


24.19 


30 


96.68 


17.92 


96.03 


19.54 


95.32 


21.13 


94.55 


22.70 


93.73 


24.24 


32 


96.66 


17.97 


96.00 


19.59 


95.29 


21.18 


94.52 


22.75 


93.70 


24.29 


34 


96.64 


18.03 


95.98 


19.64 


95.27 


21.24 


94.50 


22.80 


93.67 


24.34 


36 


96.62 


18.08 


95.96 


19.70 


95.24 


21.29 


94.47 


22.85 


93.65 


24.39 


38 


96.60 


18.14 


95.93 


19.75 


95.22 


21.34 


94.44 


22.91 


93.62 


24.44 


40 


96.57 


18.19 


95.91 


19.80 


95.19 


21.39 


94.42 


22.96 


93.59 


24.49 


42 


96.55 


18.24 


95.89 


19.86 


95.17 


21.45 


94.39 


23.01 


93.56 


24.55 


44 


96.53 


18.30 


95.86 


19.91 


95.14 


21.50 


94.36 


23.06 


93.53 


24.60 


46 


96.51 


18.35 


95.84 


19.96 


95.12 


21.55 


94.34 


23.11 


93.50 


24.65 


48 


96.49 


18.41 


95.82 


20.02 


95.09 


21.60 


94.31 


23.16 


93.47 


24.70 


50 


96.47 


18.46 


95.79 


20.07 


95.07 


21.66 


94.28 


23.22 


93.45 


24.75 


52 


96.45 


18.51 


35.77 


20.12 


95.04 


21.71 


94.26 


23.27 


93.42 


24.80 


54 


96.42 


18.57 


95.75 


20.1? 


35.02 


21.76 


94.23 


23.32 


93.39 


24.85 


56 


96.40 


18.62 


95.72 


20. 23 


34.99 


21.81 


94.20 


23.37 


93.36 


24.90 


58 


96.38 


18.68 


95.70 


20. 2S 


34.97 


21.87 


94.17 


23.41 


)3.33 


24.95 


60 


96.36 


18.73 


35.68 


20.34 


)4.94 


21.92 


94.15 


23.47 


33.30 


25.00 



60 



TOPOGRAPHIC STADIA SURVEYING 



Table 6 — Continued 

STADIA REDUCTION TABLEJ 

4 For instruments rated 1 to 100 
In the column " Hor. Dist." find 100 cos 2 a 
In the column " Diff. Elev." find: 100 sin a cos a 
Rod Vertical 



Min. 


15° 


16° 


Vi 




18° 


19° 




Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. Hor. 


Diff. 




Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. iDist. 


Elev. 





93.30 


25.00 


92.40 


26.50 


91.45 


27.96 


90.45 


29.39 


89.40 


30.78 


2 


93.27 


25.05 


92.37 


26.55 


91.42 


28.01 


90.42 


29.44 


89.36 


30.83 


4 


93.24 


25.10 


92.34 


26.59 


91.39 


28.06 


90.38 


29.48 


89.33 


30.87 


6 


93.21 


25.15 


92.31 


26.64 


91.35 


28.10 


90.35 


29.53 


89.29 


30.92 


8 


93.18 


25.20 


92.28 


26.68 


91.32 


28.15 


90.31 


29.58 


89.26 


30.97 


10 


93.10 


25.25 


92.25 


26.74 


91.29 


28.20 


90.28 


29.62 


89.22 


31.01 


12 


93.13 


25.30 


92.22 


26.79 


91.26 


28.25 


90.24 


29.67 


89.18 


31.06 


14 


93.10 


25.35 


92.19 


26.84 


91.22 


28.30 


90.21 


29.72 


89.15 


31.10 


16 


93.07 


25.40 


92.15 


26.89 


91.19 


28.34 


90.18 


29.76 


89.11 


31.15 


18 


93.04 


25.45 


92.12 


26.94 


91.16 


28.39 


90.14 


29.81 


89.08 


31.19 


20 


93.01 


25.50 


92.09 


26.99 


91.12 


28.44 


90.11 


29.86 


89.04 


31.24 


22 


92.98 


25.55 


92.06 


27.04 


91.09 


28.49 


90.07 


29.90 


89.00 


31.28 


24 


92.95 


25.60 


92.03 


27.09 


91.06 


28.54 


90.04 


29.95 


88.96 


31.33 


26 


92.92 


25.65 


92.00 


27,13 


91.02 


28. 5£ 


90.00 


30.00 


88.93 


31.38 


28 


92.89 


25.70 


91.97 


27.18 


90.99 


28.63 


89.97 


30.04 


88.89 


31.42 


30 


92.86 


25.75 


91.93 


27.23 


90.96 


28.68 


89.93 


30.09 


88.86 


31.47 


32 


92.83 


25.80 


91.90 


27.28 


90.92 


28.73 


89.90 


30.14 


88.82 


31.51 


34 


92.80 


25.85 


91.87 


27. ?3 


90.89 


28.77 


89.86 


30.19 


88.78 


31.56 


36 


92.77 


25.90 


91.84 


27.38 


90.86 


28.82 


89.83 


30.23 


88.75 


31.60 


38 


92.74 


25.95 


91.81 


27.43 


90.82 


28.87 


89.79 


30.28 


88.71 


31.65 


40 


92.71 


26.00 


91.77 


27.48 


90.79 


28.92 


89.76 


30.32 


88.67 


31.69 


42 


92.68 


26.05 


91.74 


27.52 


90.76 


28.96 


89.72 


30.37 


88.64 


31.74 


44 


92.65 


26.10 


91.71 


27.57 


90.72 


29.01 


89.69 


30.41 


88.60 


31.78 


46 


92.62 


26.15 


91.68 


27.62 


90.69 


29.06 


89.65 


30.46 


88.56 


31.83 


48 


92.59 


26.20 


91.65 


27.67 


90.66 


29.11 


89.61 


30.51 


88.53 


31.87 


50 


92.56 


26.25 


91.61 


27.72 


90.62 


29.15 


89.58 


30.55 


88.49 


31.92 


52 


92.53 


26.30 


91.58 


27.77 


90.59 


29.20 


89.54 


30.60 


88.45 


31.96 


54 


92.49 


26.35 


91.55 


27,81 


90.55 


29.25 


89.51 


30.65 


88.41 


32.01 


56 


92.46 


26.40 


91.52 


27.86 


90.52 


29.30 


89.47 


30.69 


88.38 


32.05 


58 


92.43 


26.45 


91.48 


27.91 


90.48 


29.34 


89.44 


30.74 


88.34 


32.09 


60 


92.40 


26.50 


91.45 


27.96 


90.45 


29.39 


89.40 


30.78 


88.30 


32.14 



TOPOGRAPHIC STADIA SURVEYING 



61 



Table 6 — Continued 

STADIA REDUCTION TABLE 

For instruments rated 1 to 100 
In the column " Hor. Dist." find: 100 cos 2 a 
In the column " Diff. Elev." find: 100 sin a cos a 
Rod Vertical 



'Tin. 


20° 


2] 





22° 


23° 


24° 




Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 


Hor. 


Diff. 




Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 


Dist. 


Elev. 





88.30 


32.14 


87.16 


33.46 


85.97 


34.73 


84.73 


35.97 


83.46 


37.16 


2 


88.26 


32.18 


87.12 


33.50 


85.93 


34.77 


84.69 


36.01 


83.41 


37.20 


1 


88.2* 


32.23 


87.08 


33.54 


85.89 


34.82 


84.65 


36.05 


83.37 


37.23 


6 


88. i^ 


32.27 


87.04 


33.59 


85.85 


34.86 


84.61 


36.09 


83.33 


37.27 


8 


88.15 


32.32 


87.00 


33.63 


85.80 


34.90 


84.57 


36.13 


83.28 


37.31 


13 


88.11 


32.36 


86.96 


33.67 


85.76 


34.94 


84.52 


36.17 


83.24 


37.35 


12 


88.08 


32.41 


86.92 


33.72 


85.72 


34.98 


84.48 


36.21 


83.20 


37.39 


14 


88.04 


32.45 


36.88 


33.76 


85.68 


35.02 


84.44 


36.25 


83.15 


37.43 


16 


88.00 


32.49 


86.84 


33.80 


85.64 


35.07 


84.40 


36.29 


83.11 


37.47 


18 


87.96 


32.54 


86.80 


33.84 


85.60 


35.11 


84.35 


36.33 


83.07 


37.51 


20 


87.93 


32.58 


86.77 


33.89 


85.56 


35.15 


84.31 


36.37 


83.02 


37.54 


22 


87.89 


32.63 


86.73 


33.93 


85.52 


35.19 


84.27 


36.41 


82.98 


37.58 


24 


87.85 


32.67 


86.69 


33.97 


85.48 


35.23 


84.23 


36.45 


82.93 


37.62 


26 


87.81 


32.72 


86.65 


34.01 


85.44 


35.27 


84.18 


36.49 


82.89 


37.66 


28 


87.77 


32.76 


86.61 


34.06 


85.40 


35.31 


84.14 


36.53 


82.85 


37.70 


30 


87.74 


32.80 


86.57 


34.10 


85.36 


35.36 


84.10 


36.57 


82.80 


37.74 


32 


87.70 


32.85 


86.53 


34.14 


85.31 


35.40 


84.06 


36.61 


82.76 


37.77 


34 


87.66 


32.89 


86.49 


34.18 


85.27 


35.44 


84.01 


36.65 


82.72 


37.81 


36 


87.62 


32.93 


86.45 


34.23 


85.23 


35.48 


83.97 


36.69 


82.67 


37.85 


38 


87.58 


32.98 


86.41 


34.27 


85.19 


35.52 


83.93 


36.73 


82.63 


37.89 


40 


87.54 


33.02 


86.37 


34.31 


85.15 


35.56 


83.89 


36.77 


82.58 


37.93 


42 


87.51 


33.07 


86.33 


34.35 


85.11 


35.60 


83.84 


36.80 


82.54 


37.96 


44 


87.47 


33.11 


86.29 


34.40 


85.07 


35.64 


83.80 


36.84 


82.49 


38.00 


46 


87.43 


33.15 


86.25 


34.44 


85.02 


35.68 


83.76 


36.88 


82.45 


38.04 


48 


87.39 


33.20 


86.21 


34.48 


84.98 


35.72 


83.72 


36.92 


82.41 


38.08 


50 


87.35 


33.24 


86.17 


34.52 


84.94 


35.76 


83.67 


36.96 


82.36 


38.11 


52 


87.31 


33.28 


86.13 


34.57 


84.90 


35.80 


83.63 


37.00 


82.32 


38.15 


54 


87.27 


33.33 


86.09 


34.61 


84.86 


35.85 


83.59 


37.04 


82.27 


38.19 


56 


87.24 


33.37 


86.05 


34.65 


84.82 


35.89 


83.54 


37.08 


82.23 


38.23 


58 


87.20 


33.41 


86.01 


34.69 


84.77 


35.93 


83.50 


37.12 


82.18 


38.26 


60 


87.16 


33.46 


85.97 


34.73 


84.73 


35.97 


83.46 


37.16 


82.14 


38.30 



62 



TOPOGRAPHIC STADIA SURVEYING 



Table 6 — Continued 

STADIA REDUCTION TABLE 

For instruments rated 1 to 100 
In the column " Hor. Dist." lind: 100 cos 2 a 
In the column " Diff. Elev." find: 100 sin a cos a 
Rod Vertical 



Min. 


25° 


26° 


27° 


28° 


2c 


° 




Hor. 
Dist. 


Diff. 
Elev. 


Hor. 
Dist. 


Diff. 

Elev. 


Hor. 
Dist. 


Diff. 
Elev. 


Hor. 
Dist. 


Diff. 
Elev. 


Hor. 
Dist. 


Diff. 

Elev. 





82.14 


38.30 


80.78 


39.40 


79.39 


40.45 


77.96 


41.45 


76.50 


42.40 


2 


82.09 


38.34 


80.74 


39.44 


79.34 


40.49 


77.91 


41.48 


76.45 


42.43 


4 


82.05 


38.38 


80.69 


39.47 


79.30 


40.52 


77.86 


41.52 


76.40 


42.46 


6 


82.01 


38.41 


80.65 


39.51 


79.25 


40.55 


77.81 


41.55 


76.35 


42.49 


8 


81.96 


38.45 


80.60 


39.54 


79.20 


40.59 


77.77 


41.58 


76.30 


42.53 


10 


81.92 


38.49 


80.55 


39.58 


79.15 


40.62 


77.72 


41.61 


76.25 


42.56 


12 


81.87 


38.53 


80.51 


39.61 


79.11 


40.66 


77.67 


41.65 


76.20 


42.59 


14 


81.83 


38.56 


80 46 


39.65 


79.06 


40.69 


77.62 


41.68 


76^15 


42.62 


16 


81.78 


38.60 


80.41 


39.69 


79.01 


40.72 


77.57 


41.71 


76.10 


42.65 


18 


81.74 


38.64 


80.37 


39.72 


78.96 


40.76 


77.52 


41.74 


76.05 


42.68 


20 


81.69 


38.67 


80.32 


39.70 


78.92 


40.79 


77.48 


41.77 


76.00 


42.71 


22 


81.65 


38.71 


80.28 


39.79 


78.87 


40.82 


77.42 


41.81 


75.95 


42.74 


24 


81.60 


38.75 


80.23 


39.83 


78.82 


40.86 


77.38 


41.84 


75.90 


42.77 


26 


81.56 


38.78 


80.18 


39.86 


78.77 


40.89 


77.33 


41.87 


75.85 


42.80 


28 


81.51 


38.82 


80.14 


39.90 


78.73 


40.92 


77.28 


41.90 


75.80 


42.83 


30 


81.47 


38.86 


80.09 


39.93 


78.68 


40.96 


77.23 


41.93 


75.75 


42.86 


32 


81.42 


38.89 


80.04 


39.97 


78.63 


40.99 


77.18 


41.97 


75.70 


42.89 


34 


81.38 


38.93 


80.00 


40.00 


78.58 


41.02 


77.13 


42.00 


75.65 


42.92 


36 


81.33 


38.97 


79.95 


40.04 


78.54 


41.06 


77.09 


42.03 


75.60 


42.95 


38 


81.28 


39.00 


79.90 


49.07 


78.49 


41.09 


77.04 


42.06 


75.55 


42.98 


40 


81.24 


39.04 


79.86 


40.11 


78.44 


41.12 


76.99 


42.09 


75.50 


43.01 


42 


81.19 


39.08 


79.81 


40.14 


78.39 


41.16 


76.94 


42.12 


75.45 


43.04 


44 


81.15 


39.11 


79.76 


40.18 


78.34 


41.19 


76.89 


42.15 


75.40 


43.07 


46 


81.10 


39.15 


79.72 


40.21 


78.30 


41.22 


76.84 


42.19 


75.35 


43.10 


48 


81.06 


39.18 


79.67 


40.24 


78.25 


41.26 


76.79 


42.22 


75.30 


43.13 


50 


81.01 


39.22 


79.62 


40.28 


78.20 


41.29 


76.74 


42.25 


75.25 


43.16 


52 


80.97 


39.26 


79.58 


40.31 


78.15 


41.32 


76.69 


42.28 


75.20 


43.18 


54 


80.92 


39.29 


79.53 


40.35 


78.10 


41.35 


76.64 


42.31 


75.15 


43.21 


56 


80.87 


39.33 


79.48 


40.40 


78.06 


41.39 


76.59 


42.34 


75.10 


43.24 


58 


80.83 


39.36 


79.44 


40.42 


78.01 


41.42 


76.55 


42.37 


75.05 


43.27 


60 


80.78 


39.40 


79.39 


40.45 


77.96 


41.45 


76.50 


42.40 


75.00 


43.30 



TOPOGRAPHIC STADIA SURVEYING 63 



ANDERSON'S STADIA REDUCTION TABLE 

(As prepared and in use by U. S. Geological Survey) 

Explanation of Table: Table 7 is particularly useful 
when topographic surveys of large areas are to be made. 
It was prepared by Mr. C. G. Anderson and has been 
published by the U. S. Geological Survey in a pamphlet 
entitled " Tables for Obtaining Differences of Elevation," 
1909. It is reprinted here with the permission of the 
Survey. In the U. S. G. S. pamphlet the table from 0° to 
5° angle of elevation includes rod-readings to 3500 ft. though 
here reproduced to only 2600 ft. 

The figures in the body of the table give " Differences in 
Elevation " in feet for rod-readings in feet, read on a rod held 
vertically. 

The degrees of vertical angle are printed at the top of each 
page; the minutes in the right or left-hand vertical columns. 

The figures in the top horizontal line are the rod-readings 
( = intercept times rating factor). 

The figures in the bottom horizontal line are the correct hori- 
zontal distances based on the middle (30') angle of the page. 

The horizontal distances were computed by the formula 

D=r cos 2 « (32) 

To increase the usefulness of these tables, there has been 
added, at the bottom of each page, a correction for distance 
which has been given for each departure of 10' from the angle 
for which distance is noted in the table. The basic angle 
for distance, as already stated, is in each case the half degree. 
For all vertical angles on any page or in any column less than 
this basic angle, i.e., above the 30' line, the correction will 
be positive, it will be added to the distance at the bottom of 
the page or column; and for all vertical angles larger than the 
basic angle, i.e., below the 30' line, the correction is to be sub- 
tracted. 



64 TOPOGRAPHIC STADIA SURVEYING 

The differences in elevation were computed by the for- 
mula: 

h =r sin a cos a (33) 

As elsewhere explained in this manual a somewhat closer 
approximation, when surveys are made with ordinary instru- 
ments, can be obtained by entering the table with (r+e) or 
(r+1) instead of with r. This applies both in the matter 
of difference in elevation and distance. 

This table as is seen from the above formulas was pre- 
pared for use as an approximation table and in this respect 
ranks with Table 6. When more than ordinary accuracy is 
required the corrections e cos a and e sin a can be added to the 
values taken from the table when entered with the rod- 
reading r. 

Tabular values for the omitted columns, viz.: 1000, 2000, 
and 3000, can be obtained from columns 100, 200 and 300, 
respectively, by moving the decimal point one place to the 
right. 

Tabular values beyond the range of the table can be ob- 
tained by moving the decimal point to right or left, as shown 
in the following example: 

Required the difference in elevation for an angle of 3° 16' 
for a rod-reading of 3644 ft. (i.e., intercept of half stadia 
interval, 18.22 times 200=3644 ft.). In this case (r+1) 
=3645 ft. 

For 3000 ft. (from 300 ft. moving the deci- 
mal to right) 170.7 ft. 

For 600 ft 34.1 ft. 

For 40 ft. (from 400 ft. moving the deci- 
mal point to left) 2.28 ft. 

For 5 ft. (from 500 ft. moving the deci- 
mal point two places to left) .28 ft. 

Difference in elevation 207.4 ft. 



TOPOGRAPHIC STADIA SURVEYING 65 

The distance in the case of this example is found by the 
aid of the table to be 3634 ft., as follows : 

For 3° 30' 

For 3000 ft. (from 300 ft. moving the deci- 
mal point to right) 2989 ft. 

For 600 ft 598 ft. 

For 40 ft. (from 400 ft. moving the decimal 

point to left) 40 ft. 

For 5 ft. (from 500 ft. moving the deci- 
mal point two places to left) 5 ft. 

Distance from table 3632 ft. 

For 3° 16' being 14' less than 3° 30' add: 

1.4 X36.3X.035 = 1.78 or 2ft. 

Corrected distance is 3634 ft. 



66 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 
differences in elevation 

0° 



' 


100 


200 


300 


400 


500 


600 


700 


800 


900 


1100 


1200 


1300 




1 

2 

3 

4 
5 

6 

7 
8 
9 

IO 

u 

•3 
14 
»5 

16 
«7 
18 
19 

20 

21 
22 
23 
24 
25 

26 

27 

28 
29 
30 

3> 

32 

33 
34 
35 

36 

3 l 
38 
39 
40 

*i 
42 
43 
44 
45 

46 
47 
48 
49 
50 

5» 

52 

53 

54 
55 

56 
57 
58 
59 


03 
06 
09 

>5 

18 
o- 20 
23 
26 
29 

32 

35 
3* 
41 
O 44 

047 
O 49 
052 
0-55 
O.58 

O 61 
0.64 
0.67 
0.70 
73 

0.76 
0.79 
0.81 
084 
0. 87 

0.90 
093 

0. 96 
0.99 

105 
1.08 

1. it 
1. 13 

1. 16 

1. 19 
1. 22 
i- 25 
1.28 
i-3i 

1-34 
1-3/ 
1.40 
1.42 
1-45 

1.48 
««S« 

1-54 
1-57 
I.60 

1.63 
.1.66 
1.69 
1-72 


06 
12 
18 
23 
79 

35 
41 
46 
52 
58 

0. 64 

70 
77 
81 
87 

93 
0.99 

1 05 

1. 10 
1. 16 

1. 22 

1.28 
'•34 
1.40 
i-45 

1-5' 
J-57 
1 63 
1.69 
1 74 

1.80 
1.86 
1.92 
1.98 
2.04 

2.09 

2- 15 
2.21 
2.27 
2-33 

2.38 
2-44 
2.50 
2.56 
2.62 

2.63 

«• 73 
2.79 
2.85 
2.91 

2.97 
3- 02 
3- 08 
3- H 
3- 20 

3«6 
3- 32 
3-37 
3-43 


09 
17 
26 
35 
44 

52 
61 
0.70 
079 

87 

0.96 

1 05 
1 '3 
1. 22 
1 3i 

1.40 
1.48 
1-57 
1.66 
1-75 

1.83 
1.92 
2.01 
2.09 
2.18 

2.27 
2.36 
244 
2-53 
2.62 

2.70 
•2 79 

2.88 
297 
3- 05 

3H 
3- 23 
3-32 
3- 40 
3-49 

3.58 
3-66 
3-75 
3- 84 
3 93 

4.01 
4.10 
4.19 
4.28 
4- 36 

4-45 
4-54 
4.62 
4.71 

4.80 

4.88 
4-97 
5.06 
5- 15 


1 
2 
03 
04 

6 

0.7 
08 
09 

1 
I 2 

'3 
14 
15 
1 6 

1 7 

19 
2.0 

2. 2 
2-3 

2-4 
2.6 

2 7 
' 2.8 

2.9 

3-0 
3-1 

3-3 
3-4 

3 5 

3-6 
3-7 
3-8 
4.0 
4.1 

4.2 
4-3 
4-4 
4-5 
4-7 

4.8 
4-9 
SO 
5-1 

5-2 

5-4 
5-5 
5-6 
5-7 
5-8 

5-9 
6.0 
6.2 
6-3 
6.4 

6.5 
6.6 
6.7 
6.9 


2 
03 
04 
6 

7 

09 

1. 

1 2 
' 3 
> 5 

1 6 

1 7 
» 9 

2 

2. 2 

23 
2 5 

2 6 
28 
2.9 

3-i 

3 2 
3-3 
3-5 
3 6 

3-8 

3 9 
4. i 
4.2 
4-4 

4 5 
4-7 
4 8 

4 9 

5 1 

5-2 

5-4 
5-5 
5-7 
5-8 

6.0 
6.1 
6.2 
6.4 
6-5 

6.7 
6.8 
7.0 
7- 1 
7-3 

74 
7-6 
7 7 
78 
8.0 

8.1 
8-3 
8.4 

8.6 


3 

5 
0.7 
09 

1 
1 2 
14 
16 

1 7 

« 9 

2 1 

2 3 
2 4 
2 6 

2 8 

3 

3 > 
3-3 
3-5 

3-7 
3-8 
40 

4 2 
4-4 

4 5 
4 7 

4 9 

5 1 
5-2 

5 4 
5 6 
5 8 

5 9 

6 1 

6 3 
6-5 
6.6 
6 8 
7o 

72 

7-3 
7- 5 
7-7 
7.8 

8.0 
8.2 
8.4 
8.6 
8-7 

8-9 
9.1 
9.2 
9-4 
96 

98 
9-9 

10.3 


2 
4 
6 

8 

1 

1 2 

14 
1 6 

1 8 

2 

2 ? 
2 4 
2 6 

2 8 

3 1 

3 3 
3 5 
3 7 

3 9 

4 ' 

4 3 
4-5 
4-7 

4 9 

5 1 

5-3 
5 5 
5 7 

5 9 

6 1 

6 3 
6 5 
6 7 

6 9 

7 " 

7 3 

7 5 
7-7 
&.o 

8 1 

8-3 
8.6 
8.8 
9.0 
9.2 

9.4 
9.6 
9.8 

10 

10. 2 

10.4 
10.6 
10.8 

11 

11. 2 

n. 4 
116 
11. 8 

12 


2 
05 
7 

9 

1 2 

' 4 

1 6 
• 9 

2 1 
2 3 

2 6 

2 8 
30 
3-3 

3 5 

3 7 
40 

4 2 
4 4 

4 7 

4.9 

5 ' 
5 4 

5 6 
5-8 

6 
6 3 

6 5 
67 

7 

7 2 
7 4 
7 7 

7 9 

8 1 

8 4 
8 6 

8 8 

9 1 
9 3 

9-5 
98 
10. 
10. 2 
105 

10 7 
10.9 
* 11. a 
n. 4 
11. 6 

n. 9 
12. 1 
12 3 
12 6 
12.8 

13.0 
13- 3 
13- 5 
^■7 


03 
5 

8 

1 
• 3 

1 6 

1 8 

2 1 
2 4 
2 6 

2 9 

3 ' 

3 4 
3-7 

3 9 

4 2 
4 4 
4-7 

4 5 

5 2 

5 5 

5 8 
6.0 

6 3 
6 5 

6 8 

7 1 
7 3 
7 6 

7 8 

8 1 
8 4 
8 6 

8 9 

9 2 

9 4 
9 7 
9 9 

10 2 
10.5 

10.7 

11 
11 2 

11 5 
11. 8 

12 
12 3 
12.6 

12 8 

'3- ' 

'3-4 

13 6 

13 9 

14 1 
14.4 

14-7 
14.9 

«5-2 

15 4 


3 

6 

1 
• 3 

1 6 

' 9 

2 2 
2 6 

2 9 

3 2 

3 5 

3 8 

4 2 
4-5 

4 8 

5 » 
5 4 

5 8 

6 1 
64 

6 7 

7 O 
7 4 

7 7 

8 

8 3 

8 6 
90 

9 3 
9 6 

9 9 
IO 2 
10 6 
10 9 

" 5 
n 8 
12 2 
12 5 

12 8 

»3 « 

13 4 
13 8 
14. 1 
14-4 

147 
15 
'5 4 
15-7 
16.0 

16.3 
16.6 
17.0 
*7 3 

17 6 

17 9 

18 2 
18.6 
18.9 


3 

7 

1 

1 4 

"7 

2. 1 

2 4 

2 8 

3 • 
3 5 

3 8 
42 

4 5 

4 9 

5 2 

5 6 

5 9 

6 3 

6 6 

7 O 

7 3 

7 7 

8 
8.4 

8 7 

9 ' 
9 4 
98 

10 1 

">5 

10 8 

1 1 2 
" 5 

11 9 

12 2 

12 6 
12 9 
'3 3 
'3 6 

14 

•4 3 
'4-7 

15 
15-4 
'5-7 

16. I 
16.4 
16.8 

17' 
'7 4 

178 
18.2 
18 5 
18.8 
19.2 

«9 5 
19.9 

20. 2 

30 6 


04 
0.8 
i 1 

'5 

1 9 

23 

2 6 
30 
3-4 
3-8 

4 2 

4 5 
4-9 

5 3 

5 7 

60 

6 4 
6.8 

7 2 
7 6 

7 9 
8-3 
87 
9 ' 
9 4 

9 8 

10 6 

11 i 
<« 3 

• 1 7 

•2 5 

12 9 

'3 2 

13 6 
14.0 
14.4 
'4-7 
'5 ' 

'5-5 
«5-9 

16 2 
16.6 

17 

17.4 

17 8 
18. 1 
18.5 

18 9 

19 3 
'9 7 
20.0 
20.4 
20.8 

21. 2 

21 6 
21 9 

22.3 




Horz. 
Dist. 


99^99 


J999 


299.9 


399-9 


499-9 


5999 


699.9 


799-9 


899.9 


1099.9 


1 1 99.9 


1299.9 





Hor. dist. Is for 30' point. Add or subtract .005 ft. to each 100 ft. of 
distance for each io' departure. 



TOPOGRAPHIC STADIA SURVEYING 



67 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
0° 



1400 


1500 


1600 


1700 


1800 


1900 


2100 


2200 


2300 


2400 


2500 


2600 


t 


0.4 
o.8 

I. 2 

1.6 

2.0 

2-4 
2.8 

? 3 
3-7 

4- » 

4-5 
4 9 
5-3 
5-7 
6. i 

6-5 
6.9 
7 3 

7 7 
8. i 

86 
9.0 
9-4 
98 
10. 2 

to. 6 
II 
n 4 

11 8 

12 2 

12 6 

13 .0 
'3 4 

13 8 

14 2 

14- 7 
'5 1 

15 5 
15 9 
16.3 

16.7 
17 1 
17-5 
17 9 
18.3 

18.7 
19 1 
19-5 
20.0 
20.4 

20.8 
21. 2 

21.6 

22.0 
22 4 

22.8 
23.2 
236 
24.O 


0.4 
0.9 
1-3 
17 
2. 2 

2.6 
30 
3-5 
3-9 
4.4 

4.8 

5-2 

5-7 
6.1 
6-5 

70 
7-4 
78 
8-3 
8.7 

9.2 

96 
10.0 
10.5 
10.9 

11 3 

11 8 

12 2 

12 6 

13 1 

'3 5 
14.0 
•4 4 

14 8 
15- 3 

15 7 
16. I 

16 6 

17 
17 4 

17 9 
18.3 
18.8 
19.2 
196 

20. 1 
20.5 
20. 9 
21.4 
21 8 

22. 2 

22.7 
23- 1 

23.6 

24.0 

24.4 
24.9 

25- 3 
25- 7 


05 
0.9 

1-4 
'•9 

2-3 
2.8 

>3 
3 7 
4.2 
4-7 

5-1 

5 6 
6.0 

6 5 
7.0 

7-4 
7-9 
8.4 
8.8 
9-3 

9.8 
10. 2 
10.7 
11. 2 
11. 6 

12. I 
13 6 

13 O 

13- 5 
14.0 

14.4 
'4 9 
15 4 
15- 8 
16.3 

16.7 
17.2 
17-7 
18.2 
18.6 

19. I 
19- 5 
20.0 

20 5 
20.9 

21.4 

21 9 
22.3 
22.8 
23.3 

23-7 
24.2 
24.7 

25- 1 

25.6 

26.1 
26.5 

27.0 

27.5 


OS 
1.0 
>i 
2.0 
'•5 

3-o 
3-5 
40 

4-4 
4-9 

5-4 
5 9 
6.4 
69 
74 

7 9 
8-4 
8.9 
9-4 
10. 

10.4 
10.9 

11 4 
11. 9 
12.4 

12 9 

13 3 
13- 8 

14 3 
14.8 

15 3 
158 
16.3 

16 8 

17 3 

17 8 
18.3 

18 8 
19-3 
198 

20.3 
20.7 

21. 2 
21.8 

22. 2 

22.7 
23.2 
23- 7 
24.2 
24- 7 

252 
25- 7 
26.2 
26.7 
272 

27.7 
28.2 
28.7 
29.2 


05 
1.0 
16 
2. 1 

2.6 

3-1 
3-7 
4.2 
4-7 
5-2 

5-8 
63 
6.8 
7 3 
7 9 

8-4 
8.9 
9-4 
9 9 
10.5 

11 

11 5 

12 
12.6 

13 1 

136 

14 1 
147 
15- 2 
•5 7 

16.2 

16 8 

17 3 

17 8 
18.3 

18 8 
194 
199 
20.4 
2a 9 

21-5 
22. O 

2*5 

23 O 
23.6 

24- I 
24.6 
25 I 
25.6 
26.2 

26.7 
27.2 
277 
28.3. 
28.8 

29-3 
29.8 
304 
30.9 


0.6 

1.7 
2. 2 
2.8 

3-3 
3-9 
4.4 
50 

5-5 

6. 1 

6.6 
7 2 
7 7 
8.2 

8.8 
9-4 
9 9 
10.5 

11. 1 

11 6 

12. 2 
12.7 
13 3 
138 

14.4 
14.9 

15 5 

16 

16 6 

17 « 
17 7 
18.2 
18.8 

19 3 

19.9 

20 4 

21 

21.6 

22 1 

22 7 
232 
23.8 
24-3 
24.9 

25- 4 
26.0 
26.5 
27.1 
27.6 

28.2 
28.7 
29- 3 
29.8 
3°- 4 

30.9 
3i- 5 
32.0 
32.6 


0,6 
1. 2 
1.8 
2.4 
3' 

3-7 
4-3 
4-9 

5 5 
61 

6.7 
7 3 
7 9 
8-5 
9 2 

9.8 
10.4 
11. 
11 6 
12.2 

12.8 
13-4 
14.0 
14-7 
15- 3 

•5- 9 
.6.5 
17 1 
17 7 
18.3 

18.9 
195 
20. 2 
20.8 

21 4 

22. O 

22 6 
23- 2 
23-8 
24.4 

25.O 
25.6 
26-3 
26. 9 

27-5 

28.1 
28.7 
29-3 
29.9 
30.5 

312 
3i- 8 
32 4 
33- 
33-6 

34-2 
34-8 
35-4 
36.0 


0.6 
I.J 
1-9 

2.6 
3-2 

3-8 
4-5 
5-i 
5-8 
6.4 

7.0 
7-7 
8-3 
9.0 
9.6 

IO. 2 
IO.9 

11 5 
12. 2 

12 8 

134 
14. 1 

14 7 

15 4 
16.0 

16.6 
17 3 
17 9 
18.6 
19.2 

19.8 
20.5 
21 1 

21 8 

22 4 

230 
23- 7 
24-3 
250 
256 

26.2 
26. 9 
27-5 
28.2 
28.8 

29.4 
301 
30.7 
31-4 
32.0 

32.6 
33-3 
33-9 
34-5 
35-2 

35-8 
36 5 
37-1 
37-8 


0.7 
I.J 

2.0 
2.7 
3 4 

4.0 
4-7 
5-3 
6.0 
6.7 

7-4 
8.0 
8-7 
9 4 
10. 

10.7 
n. 4 
12.0 
12.7 
13- 4 

14.0 
14.7 
15- 4 
16.0 
16.7 

17 4 
18. 1 
18.7 
19.4 
20. 1 

20.7 

21 4 

22 I 
22.7 
23- 4 

24.1 
34 7 

25- 4 

26. 1 
26.8 

27.4 
28.1 
28.8 
29.4 
30.1 

30.8 
314 
32.1 
32.8 

33-4 

34- 1 
34-8 
35-4 
36.1 
36.8 

37-5 
38.1 
38.8 
39-5 


0.7 
1-4 

2. I 
2 7 

3-5 

4.2 
4-3 

5-6 
6-3 

7.o 

7 7 
8-4 
9 1 
9.8 
10.5 

11. 2 
11. 9 
12.6 
13-3 
14.0 

14- 7 
15- 4 
16. 1 
16.8 
17- 4 

18.2 
18.8 
19- 5 

20 2 
20. 9 

21 6 
22.3 
23.0 
23- 7 
24. 4 % 

25 1 
25 8 
26.5 
27.2 
279 

28.6 

29 3 
300 
307 
31-4 

32 1 
328 
33-5 
34-2 
349 

35-6 
36.3 
37- 
37-7 
38.4 

39- * 

39-8 
405 
41.2 


07 
14 
3.2 

2.9 
3-6 

4 4 
S» 

5-8 

6 6 

7 3 

8.0 
8.7 
9-4 
10.2 
10.9 

n. 6 
12.4 
13- 1 
138 
14.6 

15-3 
16.0 
16.7 
17-4 
18.2 

18.9 
19.6 
20.4 

21. I 

21 8 

22 5 

23- 3 

24.0 

24- 7 
25- 4 

26.2 
26.9 
276 
28.4 
29.1 

29.8 
305 
St. J 

32.0 
327 

33-4 
34-2 
34-9 
35-6 
36.4 

37- I 
37-8 
38.5 
39-2 
40.0 

40.7 
41- 4 
42.2 
42.9 


0.8 
'5 
23 
3-o 
3-8 

4-5 
S3 
6.0 
6.8 
7 6 

8-3 
9- 1 
9-8 
10.6 
11. 3 

12. ( 
12 9 
. 13-6 
14.4 
15. 1 

15-9 
16.6 
17-4 
18. 1 
18.9 

19-7 
20.4 
21. 2 
21.9 
227 

23- 4 
24.2 
25.0 
25 7 
26.5 

27.2 
28.0 
28.7 
29- 5 
30.2 

31 
318 
325 
33-3 
34- 

34-8 
35-5 
363 
37- 
37-8 

38.6 
39-3 
40.1 
40.8 
41.6 

42.3 
43- 1 
43-9 
44.6 


1 
2 
3 
4 
5 

6 

7 
8 
9 
10 

ti 
12 
13 
14 
15 

16 
17 
18 
19 
20 

21 
22 
23 

24 
25 

26 
27 
28 
29 
30 

3i 
3» 
33 
34 
35 

36 
37 
38 
39 
40 

41 
4* 
43 
44 
45 

46 
47 
48 
49 
50 

51 

52 
53 
54 
55 

S6 
57 
58 
59 


'399-9 


1499* 


1599.8 


1699.8 


1799-8 


1899.8 


2099.8 


2199* 


2299.8 


2399-8 


2499.8 


2599-8 


Hon. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .005 ft. to each 100 ft. of 
distance for each 10' departure. 



68 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
1° 



200 300 400 500 600 700 800 900 1100 1200 1300 



3-49 
3-55 
3-6r 
3.66 
3-7* 
3-78 

384 
3- 90 
3- 96 
4.01 
4.07 



4.42 
4.48 
4-54 
4-59 
4- 65 

4- 71 

4-77 
4- 83 



5 00 
506 



5 '8 
5 23 



5 58 
5 64 
5 70 
5 76 
5 81 

5 8-/ 
5 93 

5 99 

6 05 
6 10 



6.22 
6.28 
6-34 
6.40 

6-45 
651 
6-57 
6.63 
668 



5-24 
5- 32 
J- 4i 
5- 50 
5-58 
5-67 

3-76 

5- 84 
5-93 



6.28 
6.37 
6.46 
6.54 

6.63 
6.72 
6.80 
6.89 
6.98 

7- 07 
7 15 
7-24 
7-33 
7- 4i 



7 59 
7.68 
7.76 
7 85 



8 20 
8 29 

«37 

8 46 
8-55 
8.63 
872 



10 8 
10. 9 



10.6 
10.8 
10.9 



"•3 
II.J 

11.6 



14 7 
14.8 

15 



>5 4 
«5 6 
>5 7 
15 8 
16.0 

16. 1 
16.3 
164 
16.6 
16.7 

16.9 
17.0 



>3-4 
13- 6 
13-8 
14.0 



14.4 
H-7 
14.9 



'5- 9 
lb. 1 
16.3 

16.5 
16.7 
16.9 
17. 1 
»7-3 

'7-5 
17.7 
17 9 



•8 5 
18.7 
18. 9 



19 9 

20 1 

20 3 

20. 6 
20.8 

21. O 



23.O 
23.2 

23- 4 

33-6 

238 
24.0 
34. 2 



14- O 
14.2 
14.4 
H-7 
14.9 



16.0 
16.2 
i6.5 
16.7 
170 



23.0 
23- 3 
23.6 



24 3 
24 6 
24 9 



27.7 
28.0 
28.3 
28.5 
28.8 



19.2 

»9 5 
19.8 
20. 1 



21.7 

22. 1 
22.4 

22.7 
23.0 

23 3 
23- 7 
24.0 

24- 3 
24. 6 

24 9 
25- 3 
256 

25- 9 

26. 2 

26 5 
26. 9 

27 2 

27 5 

27 8 

28 1 
28 5 

28 8 

29 1 

29 4 
297 

30 1 
30 4 

30 7 

31 o 
3i 3 
3' 7 

32 o 

32 3 
326 

32 9 
33-3 

33 6 



34 5 

34 

S3 

35- 
35 
36. 
36 
36. 

37 1 
37-4 
37-7 

38 o 



30 
30- 3 
307 
3' o 
3« 4 

3' 8 
32 1 
32- 4 

32 8 

33 » 

33 5 

33 «8 

34 2 
34 5 

34 9 

35 2 
35 6 

35 9 

36 3 
366 

33 9 37 o 
34- 2 37- 3 



40 5 
40.8 



1099 



1 '99 



Hor. dist. ia for 30' point. Add or subtract .015 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



69 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 















1° 
















1400 


1500 


1600 


1700 


1800 


1900 


2100 


2200 


2300 


2400 


2500 


2600 


f 


24 4 


26.2 


27.9 


29.7 


3« 4 


33-2 


366 


38.4 


40.1 


419 


43-6 


45-4 


Q 


24 8 


26.6 


28.4 


30.2 


31 9 


33-7 


37-2 


39 


40.8 


42. 6 


44 4 


46.1 


1 


25 2 


27.0 


28.8 


30.6 


32.4 


34-3 


37-9 


39-7 


4i-5 


43-3 


45 1 


46.9 


2 


2 5 6 


27- 5 


29- 3 


3" 


33- 


34-8 


38- 5 


40.3 


42. 1 


44.0 


45 8 


47.6 


3 


26. 1 


27.9 


29.8 


316 


33-5 


35-4 


39- 1 


40.9 


42.8 


44-7 


465 


48.4 


4 


26.5 


28.4 


302 


32. 1 


34 


35-9 


39-7 


41. 6 


43-5 


45-4 


47-3 


49 1 


5 


26. 8 


28.8 


30 7 


32.6 


345 


36.5 


40.3 


42.2 


44.1 


46.1 


48.0 


49-9 


6 


27 3 


29.2 


3i 2 


33- > 


35- 1 


37- 


40.9 


42.9 


44 8 


46.7 


487 


50.6 


7 


27 7 


29.7 


3>-6 


33-6 


35-6 


37. 6 


4»-5 


43 5 


45-5 


47 5 


49-4 


51-4 


8 


28.1 


30.1 


32.1 


34- 1 


36.1 


38.1 


42. 1 


44. 1 


46.1 


48. 2 


502 


522 


9 


28.5 


30 5 


32.6 


34-6 


36.6 


38.7 


42- 7 


44-8 


46.8 


48.8 


SO 9 


529 


10 


28.9 


31 


33 


35- » 


37-2 


39 2 


43 3 


45-4 


47-5 


49 5 


5« 6 


53-7 


11 


29- 3 


3>-4 


33-5 


35-6 


37-7 


39-8 


44.0 


46.1 


48.2 


SO- 3 


524 


54 4 


12 


29.7 


31.8 


34- 


36.1 


38.2 


403 


44 6 


46.7 


48.8 


509 


53- ' 


55-2 


"3 


301 


3 2 -3 


34-4 


366 


387 


40.9 


45-2 


47 3 


49 5 


51.6 


53-8 


55 9 


«4 


30 5 


32 7 


34 9 


37 1 


39 3 


41 4 


45 8 


48 


50. 2 


52 3 


54 5 


567 


'5 


30 9 


33 2 


35-4 


37-6 


39 8 


42.0 


46.4 


48.6 


508 


53 


55 2 


57-5 


16 


3« 3 


33-6 


35-8 


38. 1 


403 


42 5 


47 


49-3 


5> 5 


53 7 


56 


582 


«7 


3» 7 


34 O 


363 


38.6 


40.8 


43 ' 


47 6 


49 9 


52 2 


54-4 


56.7 


59 


18 


32 2 


34 5 


368 


39 


4i 3 


43 6 


48.2 


505 


52.8 


55- > 


57 4 


59 7 


«9 


32 6 


34 9 


37-2 


39-6 


41 9 


44.2 


48.9 


51 2 


53 5 


55 8 


58 2 


605 


20 


33 


35 3 


37 7 


40.0 


424 


44 8 


49 5 


518 


54 2 


56 5 


58 9 


61. 2 


21 


33 4 


35 8 


381 


405 


42.9 


45-3 


50 1 


52 5 


54 8 


57 2 


59 6 


62 


22 


33 8 


36 2 


38.6 


41.0 


43 4 


45 9 


50 7 


53 1 


55 5 


57 9 


60 3 


62 8 


23 


34 2 


36 6 


39 « 


4' 5 


44.0 


46.4 


5' 3 


53 7 


56.2 


58 6 


61 1 


63 5 


24 


34 6 


37 1 


39 5 


42 


44 5 


47 


5< 9 


54 4 


56 8 


59-3 


61 8 


64 3 


25 


35 


37 5 


40.0 


42 5 


45 


47 5 


52 5 


55 


57 5 


60.0 


62 5 


65.0 


26 


35 4 


37 9 


40 5 


43 O 


45 5 


48 1 


53 1 


55 6 


58.2 


60 7 


632 


65 8 


27 


35 8 


38 4 


40.9 


43 5 


46 


48 6 


53 7 


563 


588 


61 4 


64 


66 5 


28 


36 2 


38 8 


41 4 


44 O 


46.6 


49 2 


54 3 


56 9 


59-5 


62 1 


64 7 


67 3 


29 


36 6 


39 3 


41 9 


44 5 


'47 • 


49 7 


55 


57 6 


60.2 


62 8 


65- 4 


68 


30 


37 


39 7 


42 3 


45 


47 6 


50 3 


55 6 


58 2 


60. 9 


63 5 


66 2 


68.8 


3' 


37 4 


40 1 


42 8 


45-5 


48 2 


50 8 


562 


588 


61 5 


64 2 


66.9 


69.6 


32 


37 9 


40 


43 3 


46.0 


48 7 


5' 4 


56 8 


59 5 


62 2 


64.9 


67 6 


70 3 


33 


38 3 


41 


43 7 


46 5 


49 2 


5> 9 


57 4 


60. 1 


62. 9 


65 6 


68.3 


71 1 


34 


38 7 


41 4 


44 2 


47 


49 7 


52 5 


58 


60.8 


63 5 


66 3 


690 


7> 8 


35 


39 ' 


41 y 


44-7 


47 4 


50 2 


53 


58 6 


61 4 


64 2 


67 


69 8 


72 6 


36 


39 5 


42 3 


45 « 


47 9 


50 8 


53 6 


59 2 


62 


64 9 


67 7 


70 5 


733 


37 


39 9 


42 7 


45 6 


48 4 


5' 3 


54 1 


59 8 


62 7 


65 5 


68 4 


71 2 


74 1 


38 


40 3 


43 * 


46 


48 9 


5' 8 


54 7 


60. 4 


63 3 


66.2 


69. 1 


72.0 


74 8 


39 


40 7 


43 • 


46.5 


49 4 


52 3 


55 2 


61 


64.0 


66.9 


69 8 


72 7 


75-6 


40 


41 • 


44 O 


47 


49 9 


52 9 


55 8 


61.7 


64.6 


67 5 


705 


73 4' 


76 3 


4" 


4» 5 


44 5 


47 4 


50 4 


53 4 


56 3 


62 3 


65 2 


68.2 


71 2 


74 1 


77 « 


42 


419 


44 9 


47 9 


50 9 


53 9 


56 9 


62. 9 


65 9 


68 9 


71.9 


74 9 


77 9 


43 


42 3 


45 3 


48 4 


5' 4 


54 4 


57 4 


63 5 


66.5 


69 5 


72 6 


75 6 


78 6 


44 


42 7 


45 8 


48 8 


5i 9 


54 9 


58 


64 i 


67.2 


70. 2 


73 3 


76.3 


79 4 


45 


43 » 


46 2 


49 3 


52 4 


55 5 


58 5 


64.7 


67 8 


70 9 


74 


77 


80 1 


46 


43 5 


46 7 


49 8 


52 9 


56 


59 1 


653 


68 4 


71 5 


74 6 


77-8 


80 


9 


47 


43 9 


47 ' 


50 2 


53 4 


56 5 


59 7 


65- 9 


69. 1 


72.2 


75 3 


78 5 


8. 


6 


48 


44 4 


47 5 


SO 7 


53 9 


57 O 


60. 2 


66.5 


69.7 


72 9 


76 


79.2 


82 


4 


49 


44 8 


48.0 


5« 2 


54-4 


57 6 


60 8 


67 1 


703 


73-5 


76 7 


80.0 


83 


1 


50 


45 2 


48 4 


5« 


54 » 


58.1 


613 


67 8 


71.0 


74 2 


77 4 


80.7 


83 


9 


5' 


45 6 


48.8 


52 1 


55 3 


58.6 


61.8 


68 4 


716 


74-9 


78.1 


8i 4 


84 


6 


52 


46 


49 3 


52 6 


55 8 


59 l 


62.4 


69.0 


72 3 


75 5 


78 8 


82.1 


85 


4 


53 


46.4 


49 7 


53 


56 3 


59 6 


630 


69 6 


72 9 


76 2 


79 5 


82.8 


86 


1 


54 


46.8 


50. 1 


53 5 


568 


60.2 


63 5 


70 2 


73 5 


76 9 


80. 2 


83 6 


86 


9 


55 


47 2 


50 6 


53 9 


57 3 


60.7 


64 1 


70 8 


74 2 


77 6 


80.9 


84 3 


«7 


/ 


56 


47 6 


5' 


54 4 


57 8 


61 2 


64 6 


7« 4 


74 8 


78 2 


81 6 


85 


88 


4 


57 


48 


5i 5 


54 9 


58 3 


6i 7 


65 2 


72 


75 5 


78 9 


82 3 


85 8 


89 


1 


58 


48 ., 


5' 9 


55 3 


588 


62 3 


<>5 ? 


72 6 


76 i 


79 6 


83.0 


86 5 


89 


9 


59 


1399 


1499 


'599 


1699 


"799 


1899 


2098 


2198 


2298 


2398 


2498 


2598 


Hon. 
Dist. 



Hor. dist;. is for 30' point. Add or subtract .015 ft. to each 100 ft. of 
distance for each 10' departure. 



70 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 

3° 



t 


100 


200 


300 


400 


500 


600 


700 


800 


900 


1100 


1200 


1300 




o 

1 

2 
3 

4 

5 

6 

7 
8 
9 

10 
12 

•3 

• 4 
«5 

16 
17 
18 
•9 

20 

21 

22 
23 

24 
»5 

»6 
»7 

26 

2* 
30 

3» 
32 

33 

34 

35 

36 
37 
38 
39 
40 

41 

42 
43 
44 
45 

46 
47 
48 
49 
50 

5i 
52 
53 
54 
55 

56 
57 
58 
59 


3 49 
3 52 
3 55 
3- 58 
3.60 
3 63 

3 66 
3- 69 
3 72 
3 75 
3 78 

3 81 
3 84 
3 86 

3 89 
3- 92 

3-95 

3- 98 
4.01 
4.04 
4.07 

4 10 
4 «3 
4 16 
4.18 
4.21 

4 24 
4.27 
4 30 
4 33 
4 36 

4 39 
4.42 
4 44 
4-47 
4- 50 

4-53 
4- 56 
4-59 
4.62 

4- 65 

4.68 
4.71 
4-73 
4.76 
4-79 

4.82 

4- 85 
4.88 
4.91 
4-94 

4-97 
5- 00 
5.02 

5- 05 
5.08 

5- 11 
5- 14 
5- 17 
5- 20 


6 98 

7 03 
7 09 
7 15 
7 21 
7 27 

7 32 
7 38 
7 44 
7 5° 
7 56 

761 
7 67 
7 73 
7 79 
785 

7 90 

7 96 
8.02 
8.08 
8. 14 

8.19 

8 25 
8.31 
8 37 
8.43 

8 48 
8 54 
8.60 
8 66 
8 716 

8 774 
8831 
8.889 
8 947 
9. 005 

9.063 
9. 121 
9-179 
9- 237 
9- 295 

9-353 
9. 41 1 
9.469 
9- 527 
9- 585 

9.642 
9.700 
9- 758 
9.816 
9.874 

9-932 
9.990 
10.048 
10. 106 
10. 164 

10. 222 
10. 280 
10. 338 
10. 396 


1046 

10 55 
10. 64 
10.72 
10.81 
10.90 

1099 
n 07 

11 16 
11 25 
11 33 

11 42 
11 5i 
11 60 
11.68 
11 77 

11 86 

n 94 

12 03 
12. 12 
12 20 

12 29 
12.38 
12. 46 
12 55 
12. 64 

12-73 
12 81 

12 90 
12.99 

13 07 

13 16 
13 25 
13 33 
13- 42 
13-51 

13 59. 

13 68 
13-77 

13- 86 
13- 94 

14.03 
14. 12 
14. 20 

14- 29 
14.38 

14 46 

14 55 
14.64 

14 72 
14.81 

14.90 
14.98 
15- 07 
15.16 

15 25 

15 33 
15- 42 
15-51 
15-59 


14 
14 1 
14 2 
14 3 
14.4 

14 5 

14.6 
14.8 
14.9 

15 
15 1 

152 
15 3 
15 5 
15 6 
15- 7 

.58 
15 9 
16. 
16.2 
16.3 

16.4 
16.5 
16.6 
16.7 
16.8 

17 
17 1 
17.2 
17 3 
17 4 

17 5 
17 7 
178 
17.9 
18.0 

18. 1 
18.2 
18.4 
18.5 
18.6 

18.7 
18.8 
18.9 
19.0 
19.2 

19-3 
19.4 
19-5 
19.6 
19-7 

19.9 
20.0 
20. 1 
20. 2 
20.3 

20.4 
20.6 
20.7 
20.8 


17 4 
17 6 

17 7 
• 7 9 

18 
18 2 

18.3 
18.5 

18 6 
18.7 
189 

19.0 

19 2 

19 3 
19 5 
19.6 

19.8 
19.9 
20.0 
20. 2 
20.3 

20.5 
20. 6 
20.8 
20. 9 

21 2 
21.4 
21 5 
21 6 

21 8 

21.9 

22 1 
22. 2 

22 4 
22.5 

22 7 
22.8 
22.9 
23- 1 
232 

23- 4 
23-5 

23 7 
238 
24.0 

24.1 
24.2 
24-4 
24-5 
24.7 

24.8 
250 
25- 1 
25-3 
25-4 

25.6 
25-7 
25.8 
26.0 


20.9 
If. 1 

21 3 
21 4 
21 6 

21 8 

22.0 

22 1 
22 3 
22 5 
22.7 

22 8 

23 
232 
23 4 
23 5 

23 7 
23 9 
24. 1 
24.2 
244 

246 
24.8 
24.9 
25 1 
25- 3 

25-4 

25 6 
25.8 
26.0 
26. 1 

26.3 

26.5 
26.7 

26 8 
27.0 

27 2 
27-4 
27-5 
27-7 
27.9 

28.1 
28.2 
28.4 
28.6 
28.8 

28.9 
29.1 
29-3 
29.4 
29.6 

29.8 
30.0 
. 30- 1 
30- 3 
3»- 5 

30.7 
30.8 
310 

31-2 


24.4 
24.6 
24.8 
25.0 
25.2 
25 4 

•25 6 
25,8 
26. 
26.2 
26.4 

26.6 
26.8 
27 1 
27-3 
27 5 

27 7 
27.9 
28.1 
28.3 
28.5 

287 

28. 9 

29. 1 
29-3 
29-5 

297 
29.9 
30.1 
30- 3 
30- 5 

30.7 
309 
3i- 1 
31-3 
3i 5 

3i 7 
31-9 
32.1 
32.3 
32-5 

327 
32-9 
33 1 
33-3 
33-5 

33 7 
34- 

34- 1 
34-4 
34-6 

34-8 

35- 
35-2 
35-4 
35-6 

35-8 
36.0 
36.2 
36-4 


27 9 
28. 1 
28.4 
28.6 
28.8 
29.1 

29-3 
29-5 
29.8 
30.0 
30.2 

305 
30- 7 
309 
3i 1 
31 4 

31 6 

3i 8 

32 1 
323 
32.5 

32 8 
33- 
33-2 
33-5 
33-7 

33-9 

34 2 
34-4 
34-6 
34-9 

35 « 
35-3 
35-6 
35-8 
36.0 

36.2 
365 
36.7 
36- 9 
37-2 

37-4 
37-6 
37 9 
38.1 
38.3 

38.6 
38.8 
39- 
39-3 
39-5 

39-7 
40.0 
40.2 
40.4 
40.7 

40.9 
41. 1 
41-3 
41.6 


31 4 

31 7 
319 
32.2 

32 4 
32 7 

33- 
33-2 
33-5 
33-7 
34- 

34 3 

34 5 
34-8 

35 
35 3 

35 6 
35-8 
36.1 
36.3 
36.6 

36.9 
37 1 

37-4 
37 7 
37-9 

382 
384 
38.7 
39- 
39-2 

39-5 
39-7 
40.0 
40 3 
40- 5 

40.8 

4i 3 
41.6 
41.8 

42 « 
423 
42.6 
429 
43- I 

43-4 
43-6 

43 9 
44-2 
44-4 

44-7 
45- 
45-2 
45-5 
45-7 

46.0 
46.3 
46- 5 
46.8 


38.4 
38 7 
39- 
39-3 
39-6 
40.0 

40 3 
40.6 
40.9 

41 2 

41 6 

41.9 

42 2 
425 
42.8 
43- 1 

43-5 
43-8 
44. 1 

44 4 
44-7 

45 « 

45 4 
45-7 
46.0 

46 3 

46.7 

47 
47 3 
47 6 

47 9 

48 3 
48 6 

48 9 

49 2 
49 5 

49 8 
50.2 
50- 5 
50.8 
5' 1 

51-4 
518 
52. 1 
52-4 

52 7 

53 
53-4 
53-7 
54- 
54-3 

54-6 
54-9 
55-3 
55-6 
55-9 

56.2 
56.5 
56.8 
57-2 


41 9 

42 2 
42.6 
42.9 

43 2 
43 6 

43 9 
44-3 

44 6 

45 
.45-3 

45 7 
460 
46.4 
467 
47 1 

47 4 

47 8 
48.1 
485 

48 8 

49 2 
49-5 
49-9 
50.2 

50 6 

50.9 
512 
5i 6 
5i 9 
52 3 

52 6 

53 
53-3 

53 7 

54 

54-4 
54-7 
55-1 
55-4 
55-8 

56.1 

56 5 
56.8 

57 2 
57-5 

578 
58.2 
58.5 
589 
59-2 

59-6 
59-9 
60.3 
60.6 
61.0 

61.3 
61.7 
62.0 
62.4 


45-3 
45-7 
46. 1 
465 
46.8 
47.2 

47.6 

48.0 
48.4 
48.7 
49.I 

49-5 
49-9 
50.2 
50.6 

51 

5i 4 
51-7 
521 
52-5 

52 9 

53 3 
53-6 
54- 
54-4 
54-8 

55 1 
55-5 
55-9 
563 
56.6 

57 
57-4 
57-8 
582 
58.5 

58.9 
59-3 
59-7 
60.0 
60.4 

60.8 
61.2 
61.5 
61.9 
62.3 

62.7 
63.0 

63- 4 
63.8 
64. 2 

64.6 
64.9 
65- 3 
65- 7 
66. 1 

66.4 
66.8 
67.2 
67.6 


' 


Hon. 
Dist. 


99.81 


199.6 


299.4 


399 2 


499- 


599 


699 


798 


898 


1098 


1 198 


1297 





Hor. dist. Is for 30' point. Add or subtract .025 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



71 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
2° 



1400 1500 1600 1700 1800 1900 2100 2200 2300 2400 2500 2600 



55-8 
56-3 
56.7 
57-2 
57-7 
5S.1 

58.6 
59- 1 
59-5 
60.0 
60. 4 



63.2 
63.7 
64. 2 
64.6 
65.1 

656 
66.0 
66.5 
66.9 
67.4 

679 



69- 3 
697 



71.6 
72.0 



73-4 
73-9 
74-4 

74-8 
75-3 
75-8 
76.3 
76.7 

77- 1 
77-6 
78.1 
78.5 
79.O- 

79-5 
79-9 
80.4 
80.8 
81.3 

81.8 
82.2 
82.7 
83.2 



59-3 
59-8 
60.3 
60.8 



62.2 
62.7 
63.2 
637 
64. 2 

64.7 
65.2 
65- 7 
66.2 
66.7 

67.2 
67- 7 
68.2 
68.7 

69. 2 

69.6 

70. 1 
70.6 

71. 1 
71.6 



75-6 
76.0 
76.5 



77-5 
78.0 
78.5 
790 

795 
80.0 
80.5 



82.0 
82.4 
82.9 
83- 4 
83- 9 

84.4 
84.9 
85.4 
85- 9 



76.7 
774 
78.0 
78.6 
79-3 
79-9 



82.5 
83.I 

83.7 

84.4 
85.0 
85.7 



89- 5 

90.1 
90.8 
91-4 
92.0 
927 

93-3 
94.0 
94.6 
95-3 
95-9 

96.5 

97.1 
97.8 



99-7 
100.3 
101.0 



104.8 
105.4 

106. 1 
106.7 
107-3 
108.0 
108.6 

109.3 
109.9 
1 10. 5 
in. 2 



80.2 
80.9 
81.6 
82.2 
82.9 
83.6 

1*1 

84.9 
85.6 



88.9 
89.6 
90.2 

90.9 
91. 6 
92.2 
92.9 
93-6 

94.2 
94-9 
95-6 
96.2 
96.9 

97.6 
98. 2 
98.9 
99.6 
100.2 



104.2 
104.9 
105.6 
106. 2 
106.9 

107.6 
108.2 
108.9 
109.6 
no. 2 

no. 9 



114. 2 
"4-9 
115.6 
116. 2 
116. 9 

"7. 5 
118. 2 
118. 9 
ii9- 5 



108.8 
109.5 
no. 1 
no. 9 

111. J 

It2. 2 

1 12. 9 

113. 6 
"4-3 
115. o 



117. 8 

1 18. 5 

119. 2 
119. 9 
I20.6 



"3-3 
124.O 
I24.7 



123. 

I24.2 
124.9 
125.6 
I26.3 
I27.O 

127.8 
128.5 
I29. 2 
129.9 



9O.7 
9I.4 
92.2 

93- o 
93-7 
94-5 

95-2 
96.0 
96.7 
97-5 
98.2 

99.0 
99-7 
too. 5 
01. 2 
;o2.o 

02.7 
035 
04- 3 
05.0 
05.8 

06.5 
:o7- 3 

08.0 
:o8. 8 
09- 5 



29. 1 ; 
29.9 
30.6 

3*. 4 I 
32.1 

32- 9 
33-6 
34-4 
35- 1 



2495 



Hor. dist. is for 30' point. Add or subtract .025 ft. to each 100 ft. of 
distance for each 10' departure. 



72 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
3° 



200 300 400 500 600 700 800 900 



100 1200 1300 



5-23 
526 
5-29 



5- 40 
5-43 
5- 46 
5 49 
5- 52 

5-54 
S.58 
560 
5 63 

5.66 

5-69 

5 72 
5-75 
5-77 
5.80 

5-83 
5-86 
5- 89 
5 92 
5 95 

5 98 

6 01 
6.04 
6.06 
6.09 

6 12 
6.15 
6 18 
6 21 
6. 24 

6.27 
6. 30 
6 32 
6-35 
6.38 

6.41 
6-44 
6 47 
6. 50 
6.53 

6.56 
6-59 
6.61 
6.64 
6.67 

6. 70 
673 
6.76 
6.79 
6.81 



10.46 
10.51 
1057 
10.63 
10.68 
10.74 



11 to 
11. 15 
11. 20 
ti.26 
1132 

n 38 
11.44 
11.49 
"•55 
n. 61 



11.78 

11 84 
11.90 

it 96 

12 01 
12 07 
12. 13 
12 19 

12 24 
12 30 
12 36 
12.42 
12.48 

«2 53 
«2. 59 
12 65 
12.71 
12 76 

12.82 

12 88 

12.94 

13- 00 
13- 05 



•3-23 
1328 
•3-34 

'3- 40 
'3- 46 
13 5i 
>3-57 
'3- 63 

'3- 69 
«3-74 
13 80 



22.2 
22-3 
22 4 
22.5 
22.6 

22.8 
22 9 
23.O 
23- I 



23- 3 
23- 4 

23 6 
23 7 
23 8 

23 9 

24.0 

24 1 
24 3 
24 4 

24 5 
24 6 
24.7 
24.8 
250 



25 3 
25 4 
25- 5 

25 6 
25.8 
25 9 
26. o 



26.3 
26.4 
26.6 
26.7 
26.9 

27.0 
27 1 

27-3 
27.4 
27.6 

37-7 
27 9 
28.0 
28.2 
28.3 

28.4 
28.6 
28.7 
28.9 
29.0 

29.2 
29-3 
295 
29 6 
297 



30 2 
3° 3 
305 

30 6 
30 8 
30 9 



3« 3 
3« 5 
3' 6 
3i 8 



32.2 
323 
32 5 
326 

32 8 
32 9 



31-4 
31-5 
3»-7 
3i- 9 
32.0 
322 

324 
32.6 
32 7 

32 9 
33- « 

33-3 
33-4 

33 6 



34 » 
34-3 
34-5 
34 7 
34-8 



35-3 
35 5 
35 7 

35 9 
36.0 

36 2 
36 4 
36 6 

36 7 

36 9 

37 » 
37 2 
37 4 

37 6 
37 8 
37 9 
38.1 



38.5 

38 6 
38.8 
39- o 
39-2 

39 3 
39 5 
39-7 
39 8 



36.6 
36.8 
37- o 
37-2 
37 4 
37 6 

37 8 

38.0 
38.2 
38.4 

38 6 



39-2 
39-4 
39-6 

39 8 
40.0 

io. 2 
40.4 

40 6 

40.8 

41 o 



42 2 
42 4 
42 7 



43 3 
43 5 
43 7 

43 9 
44. 1 

44 3 
44 5 



45 3 
45 5 

45 7 

45-9 
46. 1 
46- 3 

46 5 
46.7 



42.0 
42.3 
42.5 
42 7 



43-2 
43-4 
43-7 
43-9 
44 1 



45-5 
45-7 
46 o 

46 2 
46.4 

46.7 
469 

47 1 
47 4 
47 6 

47 8 
48. 1 

48 3 

48 5 
48.7 

49 o 
49 2 
49 4 
49 7 
49 9 



50 4 
50 6 
50 8 
5» » 



5i 7 
52.0 
52 2 

52 4 

52 7 
529 

53 > 
53 4 

53 6, 

53 8 
54- 1 
54-3 
54-5 

54 7 

55 o 
55 2 
55 4 



54 3 

54 6 
54-8 

55- « 

55 4 

55 6 
55-9 

56 1 

56.4 
567 
569 

57 2 
57 4 

57 7 
580 

58 2 
58.5 
587 



61 o 
61.3 
61.6 
61. 9 
62.3 

62.6 

62 9 
63- 2 
63- 5 
63.8 

642 
64-5 
64.8 
65.1 
65 4 



68.9 
69. 2 

69.6 
69.9 
70 2 



72 1 
72 4 

72 7 
73; ' 

73 4 

737 

74 o 
74 3 
74.6 



02.7 

63.1 


07. 
68. 


63.4 


68. 


63.8 


69. 


64.1 


69. 


64.4 


69. 


64.8 


70. 


65.1 


70. 


65. 5 


7»- 


65.8 


7i. 


66.2 


71- 


66.5 


72. 


66.9 


72. 


67.2 


72. 


67.6 


73- 


67.9 


73- 


68.3 


74 


68.6 


74- 


69.0 


74 


69 3 


75- 


69.6 


75- 


70 


75 


70.4 


76. 


70.7 


76. 


71 


77 



73 5 
73 8 
74-2 
74-5 
74^9 



78 6 
78.3 

78 7 

79 o 
79-4 
79-7 
80.0 



Hor. dist. is for 30' point. Add or subtract .035 ft. to each 100 ft. of 
distance for each io' departure. 



TOPOGRAPHIC STADIA SURVEYING 



73 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
3° 



1400 


1500 


1600 


1700 


1800 


1900 


2100 


2200 


2300 


2400 


2500 


2600 


f 


73-2 
73-6 
74- o 
74-4 
74-8 
75-2 

75-6 
76.0 
76.4 
76.8 
77 2 

77 6 
78.0 
78.4 
78.8 
79-2 

796 
80.0 
80.5 
80.9 
81.3 

81 7 

82 1 
82 5 

82 9 

83 3 

83 7 
841 

84 5 

84 9 

85 3 

85 7 

86 1 
86.5 
86.9 

87 3 

87 7 
88. 1 

88 5 
88 9 
89.4 

89.7 

90 2 
90.6 

91 
91 4 

91 8 

92 2 

92 6 

93 
93 4 

93 8 

94 2 
94.6 
95- 

95 4 

95-8 

96 2 
96.6 

97 O 


78.4 
78.8 
79-3 
797 
80.1 
80.6 

81 
81.4 
81.9 
82.3 
82.7 

83.2 
83.6 
84.0 
84- 5 
84.9 

85.3 
85.8 

86 2 
86.6 

87 1 

87 5 

87 9 

88 4 
88.8 

89 2 

89 7 

90 1 

90 5 

91 
91 4 

91 8 

92 3 

92 7 

93 « 

93 6 

94 

94 4 

94 8 
95-3 

95 7 

96 2 
96.6 

97 
97 5 

97 9 

98 3 

98 8 

99 2 
99 6 

100. 1 

100 5 

100 9 

101 4 

101 8 

102 2 

102 6 

103. 1 
'03. 5 

104. 


83 
84 
84 
85 
85 
85 

86 
86 
87 
87 
88 

88 
89 
89 
90 
90 

91 
9' 

92 
92 
9? 

93 
93 
94 
94 
95 

95 
96 
96 
97 
97 

98 
98 
98 
99 
99 

100 
100 

IOI 

1 01 

102 

103 
103 

104 
104 

104 
'05 
«»3 
106 

106 

1 07 
107 
108 
.08 
109 

109 
109 
1 10 
1 10. 


6 
1 
6 

5 
9 

4 
9 
3 

8 

2 

7 
2 
6 
1 
6 


5 

4 
9 

3 

8 
3 

7 
2 

6 

6 

5 

4 
9 
3 
8 

3 
7 

2 
6 

6 

5 


4 

9 
3 

8 
3 

7 

2 
6 
1 
6 

5 
9 
4 
9 


88.8 

89- 3 
89.8 
90.4 
90.8 
9'-3 

91. 8 
92.3 
92.8 
93-3 
93-8 

94-3 
94-7 
95-2 
95 7 
96.2 

96.7 
97.2 
97-7 

98 2 
98.7 

99 2 
99-7 

100 2 
100. 6 

101 1 

101 6 

102 1 
102 6 

103. 1 
103.6 

104 1 

104. 6 

105. 1 
105.6 
106 

1065 
107.0 
•07 5 
108.0 
108.5 

109.0 
109.5 
no 
no 5 
no. 9 

in 4 
in 9 

112 4 
112 9 
"3 4 

"3 9 
114 4 
1 14. 9 
"5-4 
.158 

116. 3 

116. 8 
117 3 

1 17. 8 


94 
94 
95 
95 
96 
96 

97 
97 
98 
98 
99 

99 

100 

IOI 

102 
102 
103 
104 
104 

105 
105 
106 
106 
107 

10/ 
108 
108 
109 
109 

1 10 

1 10 

1 1 1 

1 1 1 
112 

1 12 
"'3 
•'3 

114 
114 

"5 
i>5 
116 
117 
117 

Il8 

118 
119 
119 
120 

122 
'23 

•23 

124 

124 


1 
6 

6 
2 
7 

2 
7 
2 
8 
3 

8 
3 
8 
4 
9 

4 
9 
4 

4 



5 

6 

6 
1 

6 

2 

7 

7 

8 
3 

8 
3 
8 
4 
9 

4 
9 
4 

5 


5 

5 

6 
6 
7 

2 

7 
2 
7 


99 
99 
100 
100 

IOI 

102 

102 
• 03 
•03 
104 
104 

'05 
•05 
106 
107 
.07 

108 
108 
109 
109 
no 

no 
1 1 1 

112 
"3 

iij 
114 

ii 4 

"5 
"5 

116 
1.6 
117 
III 

118 

119 
119 

121 

121 

122 
122 
•23 
124 

•24 

•25 
•25 
126 
126 

127 
127 
128 
128 
129 

'30 
I30 
•31 

•3i 


3 
9 
4 
9 
5 


6 

2 
7 
2 
9 

3 
9 
4 

5 

1 
6 

2 
7 
3 

8 
4 
9 
5 


6 

1 
7 

2 
8 

3 
9 
4 
O 
5 

6 

2 

7 
3 

8 
4 
9 
5 


5 

6 

7 

3 
8 
4 
9 
5 



6 

7 


109.8 
1 10. 4 

III.O 

m. 6 
112. 2 

112.8 

"3-4 
1 14.0 

114. 6 

1 15. 2 
115.8 

116. 4 
1170 

1 17. 6 

118. 3 
1 18. 9 

"9 5 
120. 1 
120.7 
121. 3 
121. 9 

122.5 
123- 1 
•23-7 
•24 3 
1249 

•25. 5 
126. 1 

126 7 

127 4 
128.0 

128.6 
129.2 
129.8 
•30 4 
i3'-o 

i3« 6 
132 2 
1328 
•33-4 
•34- 

134-6 
•35-2 
•35-8 
•36.4 
<37 « 

«37 7 
•38.3 
138.9 
•39-5 
140. 1 

140.7 
«4> 3 
141. 9 
•42-5 
•43-1 

'43-7 
•44-3 
144.9 
•45-5 


••5 
••5 
116 
116 
117 
118 

III 

119 
120 
120 
121 

122 

122 
•23 
•23 
124 

•25 
'25 
126 
127 
127 

128 
129 
129 
•30 
•30 

•3' 

132 
•32 
•33 
'34 

•34 
'35 
■ 36 
'36 
^37 

137 
'38 
'39 
'39 
140 

141 
141 
142 
142 
'43 

•44 
'44 
'45 
146 
146 

•47 
148 
148 
•49 
149 

'50 
151 

151 

152 


O 
6 

3 
9 

5 
2 

8 

4 

7 
3 

6 
3 
9 

5 

2 
8 
4 

7 

3 

6 
2 
9 

5 
2 

8 
4 

7 
3 


6 

2 

9 

5 

1 
8 
4 

7 
3 
9 
6 

2 
8 
5 
1 
8 

4 

6 
3 
9 

6 

2 
8 
5 


120. 2 
120.9 
121. 5 
122.2 
122.9 
"3-5 

124. 2 
124.9 
125.5 
126.2 
126.9 

127.5 
128.2 
128.9 

'295 
130. 2 

130.8 
•3'-5 
132.2 
132.9 
133- 5 

'34-2 
•34- 9 
•35- 5 
136.2 
136.8 

137 5 

138.2 
138.8 
'39-5 
140.2 

140.8 
Hi 5 
142. 1 
142 8 
143-5 

144. 1 
1448 
'45-5 
146. 1 
146.8 

147-4 
148. 1 
148.8 
149.4 
150. l 

1508 
'51-4 
152.1 
152-7 
•53-4 

154- « 
1547 
'55-4 
156. 1 
1567 

«57-4 
158. 1 
•58-7 
•59-4 


125 
126 

126 
127 
128 
128 

129 
'30 
'3' 
'3' 
•32 

•33 
'33 
'34 
'35 
•35 

•36 
'•37 
'37 
•38 
'39 

140 
140 
141 
142 
142 

•43 
144 
'44 

us 

146 
144 

'47 
,48 
'49 
'49 

'50 
'5' 
•5' 
'52 
'53 

•53 

'54 
•55 
«55 
r 5 6 

•57 
•58 
'58 
'59 
160 

160 
161 

162 
162 
'63 

164 
164 
•65 
166 


4 
1 
8 
5 
2 
9 

6 

3 


7 
4 

I 
8 
5 
2 
8 

5 
2 
9 
6 
3 



7 
4 

7 

5 
2 

8 
5 
2 

9 
6 
3 

7 

4 

8 
5 

2 

9 
6 
2 
9 
6 

3 


7 
4 
1 

8 
5 
2 

9 

5 

9 
6 
3 


130 
•3i 

•32 
•32 

•33 
•34 

•35 
•35 
•36 
n7 
•37 

•38 
•39 
140 
140 
141 

142 
•43 
•43 
•44 
•45 

•45 
146 
•47 
148 
.48 

'49 
'50 
'50 
'5' 
152 

'53 
153 
'54 
'55 
'56 

•56 

'57 
'58 
'58 
'59 

160 
161 
161 
162 
'63 

•63 
164 
•65 
166 
166 

167 

168 
168 
169 
170 

171 
171 
172 
'73 


7 
4 

8 
6 
3 


7 

4 
2 
9 

6 
3 

1 
8 
5 

2 


7 

4 

I 

8 
6 
3 

7 

4 

2 
9 
6 
3 

8 

5 
2 


7 
4 
I 
8 
6 

3 

7 
4 
2 

9 
6 
3 

8 

5 
2 
9 
6 
4 

1 
8 
5 
3 


135-9 
136.6 
137-4 
138. 1 . 
138.9 
139-6 

140.4 
141. 2 
141.9 
142.6 
143-4 

1442 
1449 
•45-7 
146.4 
147-2 

147-9 
148.7 
149-4 
150.2 
150- 9 

»5«-7 
«52-4 
'53-2 
»53-9 
154-7 

«55-4 
156.2 
•56.9 
•57 7 
•58 4 

•59-2 
•59-9 
160.7 
161. 4 
162. 2 

162.9 
163.7 
164.4 
165. 2 
165.9 

166.7 
167.4 
168.2 
168.9 
169.7 

170.4 
171. 2 
171. 9 
172.7 
173-4 

174.2 
'74-9 
•75-7 
176.4 
177.2 

'77-9 
178.7 
•79-4 
180.2 


O 

t 

3 

3 
4 
5 

6 
7 
8 
9 

(O 

it 

(2 

'3 
'4 
«5 

16 
«7 
18 
'9 
20 

21 
22 
23 
24 

25 
26 

27 
28 
29 
30 

3» 
32 
33 
34 
35 

36 
37 
38 
39 
40 

41 

42 
43 
44 
45 

46 
47 
48 
49 
SO 

5» 

5* 
53 
54 
55 

56 
57 
58 
59 


•395 


•494 


'594 


1694 


•793 


'893 


2092 


2192 


2291 


239' 


2491 


2590 


Horz. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .035 ft. to each 100 ft. of 
distance for each io' departure. 



74 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
4° 



t 


100 


200 


300 


400 


500 


600 


700 


800 


900 


1100 


1200 


1300 




o 


6.96 


• 3- 92 


20.87 


27.8 


34-8 


41.8 


48.7 


55-7 


62.6 


76-5 


83.5 


905 




I 


6.99 


13- 98 


20.96 


28.0 


1 34-9 


41.9 


48.9 


55-9 


62. 9 


76.9 


83-8 


90.8 




2 


7.02 


14- «8 


21.05 


28.1 


35-1 


42.1 


49-1 


56.1 


63.1 


77.2 


84.2 


91.2 




3 


7- 05 


14.09 


21.14 


28.2 


35-2 


42-3 


49-3 


564 


63- 4 


77-5 


84- 5 


91.6 




4 


7.08 


14- >5 


21.22 


28.3 


35-4 


42-4 


49-5 


56.6 


63-7 


77.8 


84.9 


92.0 




5 


7.10 


14.21 


21. 31 


28.4 


35-5 


42.6 


49-7 


56.8 


63- 9 


78.1 


85.2 


92.3 




6 


7- 13 


14. 26 


21-39 


28.5 


35-7 


42.8 


49-9 


57- 1 


64. 2 


78.4 


85.6 


92.7 




7 


7.16 


14- 32 


21.48 


28.6 


35-8 


43- 


50. 1 


57-3 


64.4 


78.8 


85- 9 


93-1 




8 


7.19 


14.38 


21-57 


28.8 


35-9 


43- 1 


50.3 


57-5 


64.7 


79. 1 


86.3 


93-5 




9 


7. 22 


14.44 


21.65 


28.9 


36.1 


43-3 


50-5 


57-7 


65.0 


79-4 


86.6 


93-8 




IO 


7- 25 


14.49 


21.74 


29.0 


36.2 


43-5 


50.7 


58.0 


65.2 


79-7 


87.0 


94.2 




n 


7.28 


"4-55 


21.83 


291 


36.4 


43-7 


509 


58.2 


65-5 


80.0 


87.3 


94.6 




13 


7- 30 


14.61 


21.91 


29. 2 


36.5 


43-8 


51- 1 


58.4 


65-7 


80.3 


87.6 


95- 




13 


7-33 


14.67 


22.00 


29-3 


36.7 


44.0 


5i-3 


58.7 


66.0 


80.7 


88.0 


95-3 




«4 


7.36 


14.72 


22.08 


29.4 


36.8 


44.2 


51-5 


58.9 


66.3 


81.0 


88.3 


95-7 




'5 


7-39 


14.78 


22.17 


29.6 


37- 


44-3 


51-7 


59- 1 


66.5 


8.-3 


88.7 


96.1 




16 


7.42 


14.84 


22. 26 


29- 7 


37-1 


44-5 


51-9 


59-4 


66.8 


81.6 


89.0 


96.4 




«7 


7-45 


14.90 


22.34 


29.8 


37-2 


44-7 


521 


59-6 


67.0 


81.9 


89.4 


96.8 




18 


7.48 


14- 95 


22.43 


29.9 


37-4 


44-9 


52.3 


59-8 


67-3 


82.2 


89.7 


97-2 




«9 


7-51 


15- 01 


22.52 


30.0 


37-5 


45- 


52-5 


60.0 


67-5 


82.6 


90.1 


97.6 




20 


7-53 


15- 07 


22.60 


30.1 


37-7 


45-2 


52- 7 


60.3 


67.8 


82.9 


90.4 


97-9 




21 


7.56 


15-13 


22. 69 


30-3 


37-8 


45-4 


52.9 


60.5 


68.1 


83.2 


90.8 


98.3 




22 


7-59 


15.18 


22.78 


304 


38.0 


45-6 


53-1 


60.7 


68.3 


83- 5 


91. 1 


98.7 




23 


7.62 


15-24 


22.86 


30.5 


38.1 


45-7 


53-3 


61.0 


68.6 


83-8 


91.4 


99. 1 




24 


7- 65 


15- 30 


22.95 


30.6 


38.2 


45-9 


53-5 


61.2 


68.8 


84. 1 


91.8 


99-4 




25 


7.68 


1536 


23- 03 


30- 7 


38.4 


46.1 


53-7 


61.4 


69.1 


84- 5 


92. 1 


99-8 




26 


7-71 


15-41 


23- 12 


30.8 


38.5 


46. 2 


53-9 


61.7 


69.4 


84.8 


92-5 


100. 2 




27 


7-74 


15- 47 


23-21 


30.9 


38.7 


46.4 


54- 1 


61. 9 


69.6 


85.1 


92.8 


100.6 




28 


7.76 


15- 53 


23- 29 


3i- 1 


38.8 


46.6 


54-4 


62. 1 


69.9 


85-4 


93-2 


100.9 




29 


7- 79 


15- 59 


23-38 


312 


39- 


46.8 


54-6 


62.3 


70.1 


85-7 


93-5 


101.3 




30 


7.82 


15.64 


23- 46 


31-3 


39-1 


46.9 


54-8 


62.6 


70.4 


86.0 


93-9 


101. 7 




3' 


7.85 


I5-70 


23-55 


3i-4 


39-3 


47. 1 


55- 


62.8 


70.7 


86.4 


94.2 


102. 1 




32 


7.88 


1576 


23- 64 


31-5 


39-4 


47-3 


55-2 


63.0 


70.9 


86.7 


94-5 


102. 4 




33 


7.91 


15.82 


23.72 


31.6 


39-5 


47-4 


55-4 


63- 3 


71.2 


87.0 


94-9 


102.8 




34 


7-94 


15-87 


23.81 


31-7 


39-7 


47.6 


55-6 


63-5 


7'-4 


87-3 


95-2 


103. 2 




35 


7-97 


"5-93 


23.90 


31-9 


39-8 


47-8 


55-8 


63-7 


71- 7 


87.6 


95-6 


103.6 




36 


7-99 


15-99 


23.98 


32.0 


40.0 


48.0 


56.0 


64.0 


71-9 


87.9 


95-9 


103-9 




37 


8.02 


16.05 


24.07 


32.1 


40.1 


48. 1 


56.2 


64. 2 


72.2 


88.2 


96.3 


104.3 




38 


8.05 


16.10 


24-15 


32.2 


40.3 


48.3 


56.4 


64.4 


72-5 


88.6 


96.6 


104.7 




39 


8.08 


16.16 


24.24 


323 


40.4 


48.5 


56.6 


64.6 


72.7 


88.9 


97.0 


105.0 




40 


8. 11 


16.22 


24- 33 


32-4 


40.5 


48.7 


56.8 


64.9 


73- 


89.2 


97-3 


105.4 




4» 


8. 14 


16.27 


24.41 


32-6 


40.7 


48.8 


57- 


65.1 


73-2 


89- 5 


97-7 


105.8 




42 


8.17 


16.33 


24.50 


32-7 


40.8 


49.0 


57-2 


65- 3 


73-5 


89.8 


98.0 


106. 2 




43 


8.20 


16.39 


24.58 


32-8 


41.0 


49.2 


57-4 


656 


73-8 


90. 1 


98.3 


106.5 




44 


8.22 


16.45 


24.67 


32-9 


41. 1 


49-3 


57-6 


65.8 


74.0 


90.5 


98.7 


106.9 




45 


8.25 


16.50 


24.76 


33- 


4i-3 


49-5 


57-8 


66.0 


74-3 


90.8 


99.0 


107.3 




46 


8.28 


16.56 


24.84 


33- » 


41.4 


49-7 


58.0 


66.2 


74-5 


91. 1 


99-4 


107.7 




47 


8.31 


16.62 


24-93 


33-* 


41.6 


49-9 


58.2 


66.5 


74.8 


91.4 


99-7 


108.0 




48 


8-34 


16.68 


25.02 


33-4 


4i-7 


50.0 


58.4 


66.7 


75- 


91.7 


100. 1 


108.4 




49 


8-37 


16.73 


25. 10 


33-5 


41.8 


50.2 


58.6 


66.9 


75-3 


92.0 


100.4 


108.8 




50 


8.40 


16.79 


25- 19 


33-6 


42.0 


50.4 


58.8 


67.2 


75-6 


92.4 


100.8 


109. 1 




51 


8.43 


16.85 


25.27 


33-7 


42.1 


50.5 


59- O 


67-4 


75-8 


92-7 


IOI. 1 


109- 5 




52 


8-45 


16.91 


25- 36 


33-8 


4^-3 


50.7 


59-2 


67.6 


76.1 


93- 


101.4 


109.9 




53 


8.48 


16.96 


25-45 


33-9 


42.4 


50.9 


59-4 


67.9 


76.3 


93-3 


101. 8 


1 10. 3 




54 


8. 5 i 


17.02 


25- 53 


34- 


42.6 


5i- 1 


59-6 


68. 1 


76.6 


93-6 


102. 1 


no. 6 




55 


8-54 


17.08 


25.62 


34-2 


42-7 


512 


59-8 


68.3 


76.9 


94-9 


102.5 


III.O 




56 


8-57 


17.14 


25.70 


34-3 


42.8 


51-4 


60.0 


68.5 


77-1 


94.2 


102.8 


in. 4 




57 


8.60 


17.19 


25-79 


34-4 


43- 


516 


60. 2 


68.8 


77-4 


94.6 


103.2 


in. 8 




58 


8.63 


17. 26 


25-87 


34-5 


43- 1 


51.8 


60.4 


69.0 


77.6 


94-9 


103- 5 


112. 1 


59 


8.65 


17.31 25.96 


34-6 


43-3 


51-9 


60.6 


69. 2 


77-9 


95-2 


103.8 


112.5 | 


Horz. 
Dist. 


99- 38 


98.8 


298. 1 1 


397-5 


496.9 


596 


696 


795 


894 1 


1093 


1 193 


1292 





Hor. dist. is for 30' point. Add or subtract .045 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



75 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 



1400 


1500 


1600 


1700 


1800 


1900 


2100 


2200 


2300 


2400 


2500 


2600 


f 


97-4 
97.8 
98.2 
98.6 
99.0 
99-4 

99-8 
100. 2 
100.6 
101.0 
lot. 5 

101.9 

102.3 
102.7 
103. 1 
103.5 

103.9 
104.3 
104.7 
105. 1 
105.5 

105.9 
106.3 
106.7 

107. 1 

«07-5 

107.9 
108.3 
108.7 

109. 1 
109.5 

109.9 

1 10. 3 
110.7 

111. 1 
mi. 5 

in. 9 

1 12. 3 
112.7 
113- ' 
1 «3- 5 

"3-9 
"4-3 
114. 7 
115- 1 
"5-5 

"5-9 
116.3 
116.7 
117. 1 
"7-5 

117.9 
118.3 
118.7 
119. 1 
119- 5 

120.0 
120.4 
120.8 
121. 2 


104.4 
104.8 
105. 2 
J05.7 
106. 1 
106.5 

107.0 
107.4 
107.8 
108.3 
108.7 

109. 1 
109.6 
no. 
no. 4 
110.9 

in. 3 
in. 7 
112. 2 
112. 6 
113-0 

1 13- 4 
II3-9 
1 14- 3 
114.7 
115- 2 

"5-6 
116.0 
116. 5 
116. 9 
1 17- 3 

117.8 
118. 2 
118.6. 
119. 
"9- 5 

«i9-9 
120.3 
120.8 

121. 2 
121. 6 

122. 1 
122.5 
122.9 
123- 4 
123.8 

124.2 
124.7 

125. 1 
125-5 
125- 9 

126. 4 
126.8 
127.2 
127.7 
128. 1 

128.5 
128.9 
129.4 
129.8 


in. 3 
in. 8 
112.3 
112.7 
113. 2 
1 13. 6 

114. 1 
114.6 
115-0 
II5-5 
"5-9 

116. 4 

1 16. 9 
1 17- 3 

117. 8 

118. 2 

118. 7 

119. 2 

119. 6 

120. 1 
120.6 

121. 
121. 5 
121. 9 
122.4 
122.8 

1 23- 3 
123.8 
124.2 
124.7 

125. 1 

125.6 
126. 1 
126.5 
127.0 
127.4 

127.9 

128.4 
128.8 

129-3 
129.7 

130.2 
130.7 
1)1.1 

131-6 
132.0 

»32-5 

133- 9 
133- 4 
133- 9 
134- 3 

134- 8 
>35- 2 
135- 7 
136.2 
136.6 

137.1 

'37-5 
138.0 
138.5 


1 18. 3 

1 18. 8 
"9-3 

1 19. 8 
120.3 
120.7 

121. 2 

121. 7 

122. 2 
122. 7 
123.2 

123.7 
124.2 
I24.7 

125. I 
125.6 

126. I 
126.6 

127. I 
127.6 

128. I 

128.6 

129. I 

129- 5 
130.0 

130.5 

i3'-0 

I3I-5 
132.0 
132.5 
133- 

«33- 5. 
133- 9 
134- 4 
134- 9 
135- 4 

135- 9 
136.4 
1369 
137.4 
«379 

138.3 
138.8 
139- 3 
139 8 
1403 

140.8 
I4I-3 
141. 8 
142.2 
142.7 

143- 2 
143- 7 
144.2 
144- 7 
145-2 

145-7 

146. 1 
146.6 

147. 1 


125.2 
125.8 
126.3 
126. 8 
127-3 
127.8 

128.4 
128.9 
129.4 
129.9 
130.4 

131-0 
I3I-5 
132.0 
132.5 
133- O 

133-5 

134- 1 
134.6 

135- 1 
135- 6 

136.1 
136.7 
137-2 
137- 7 
138.2 

138.7 
139- 2 
139- 8 
140 3 
140. 8 

141- 3 
141. 8 
1423 
142.9 
143- 4 

143- 9 
144.4 
144.9 
145-4 
146.9 

1465 
147.0 
147-5 
148.0 
148.5 

149. 1 
149.6 

150. 1 
150.6 

151. I 

1516 
152.2 
J52. 7 
153- 2 
153-7 

154-2 
154-7 
155-2 
155-8 


132.2 
132.8 
133' 3 
133- 9 
134-4 
134- 9 

«35-5 
136.0 
136.6 
137. 1 
»37-7 

138.2 
138.8 
1393 
139.9 
140.4 

141. 
I4I-5 
142. 1 
142.6 
143-2 

143-7 

144.2 
144.8 
145-3 
145-9 

146.4 
147- 
147-5 
148. 1 
148.6 

149.2 
149- 7 
150.3 
150.8 
I5I-3 

I5« 9 

1524 
153 
•53-5 
154- 1 

154.6 
155-2 
155-7 
156.2 
156.8 

«57-3 
> 57- 9 
158.4 
159- 
159-5 

160. 1 
160.6 

161. 2 
161.7 
162.2 

162.8 
1633 
163- 9 
164.4 


146. 1 
146.7 
147-3 
147-9 
148.6 
149-2 

149-8 
150.4 
151-0 
151.6 
152.2 

152.8 
153-4 
154.0 
154.6 
'55-2 

155-8 
156.4 
I57-0 
157.6 
158.2 

158.8 
159-4 
160.0 
160.6 
161. 2 

161. 8 

162. 4 

163. 1 
163.7 
164- 3 

1649 
i6 5 -5 
166. 1 
166.7 
1673 

1679 
168.5 
169. 1 
169.7 
1703 

170.9 
I7I-5 
172. 1 
172.7 
•73-3 

>73- 9 
'74-5 
175- 1 
175-7 
176.3 

176.9 

>77- 5 
178. 1 
178.7 
179- 3 

179.9 
180.5 
181. 1 
•181. 7 


153- 1 
153-7 
154-4 
155- 
155-6 
156.3 

156.9 
157- 5 
158.2 
158.8 
159-4 

160. t 
160.7 
161. 3 
162.0 
162.6 

163.2 
163- 9 
1645 
165. 1 
165.8 

166.4 
167.0 
167.6 
168.3 
168.9 

169.6 
170.2 
170.8 
17'. 4 
172. 1 

172.7 
'73-3 
174.0 
174.6 
175-2 

175-9 
176.5 
177. 1 
177.8 
178.4 

179- 

179.7 
180.3 
180.9 
181. 6 

182.2 
182.8 
183-4 
184. 1 
184.7 

185.3 
186.0 
186.6 

187.2 
187.9 

188.5 
189. 1 
189.8 
190.4 


160.0 
160.7 
161. 4 
162. 
162.7 
1634 

164.0 
164.7 

1653 
166.0 
166.7 

167.3 
168.0 
168.7 
169.3 
170.0 

170. 6 
I7I-3 
172.9 
172.6 
173-3 

173-9 
1746 
175-3 
175-9 
176.6 

177-3 
177-9 
178.6 
179.2 
189.9 

180.6 
181. 2 
181. 9 
182.5 
183.2 

1839 
184- 5 
185.2 
185.8 
186.5 

187.2 
187.8 
188. 5 
189.1 
189.8 

190.5 
191. 1 
191. 8 
192.4 
193- 1 

193-8 
194.4 
195- 1 
'95-7 
196.4 

197. I 

197-7 
198.4 
199.0 


167.0 

167.7 
168.4 
169. 1 
169.8 
170.5 

171. 2 
171. 8 
1725 
173-2 
173-9 

174.6 
175-3 
176.0 
176.7 
177-4 

178. 1 
178.8 
179- 4 
180. 1 
180.8 

181. 5 
182.2 
182.9 
183.6 
184.3 

185.0 
185.7 
186.3 
187.0 
187.7 

188.4 
189.1 
189.8 
190.5 

191. 2 

i9«-9 

192. 6 
193-2 
193 9 
194.6 

195-3 
196. 
196.7 
197-4 
198. 1 

198.7 
199.4 
200. 1 
200.8 
201.5 

202. 2 
202. 9 
203.6 
204. 2 
204.9 

205.6 
206.3 
207.0 
207.7 


174- 
174- 7 
175-4 
176. 1 
176.8 
1776 

178.3 
1790 
179-7 
180.4 

181. 2 

181. 9 

182.6 
183-3 
184.0 
184.7 

185.5 
186.2 
186.9 
187.6 
. 188.4 

189. 1 
189.8 
1905 
191. 2 
192.0 

192.7 
193-4 
194. 1 
194.8 
»95-5 

1963 
197.0 
197-7 
198.4 

199. 1 

199.8 

200. 6 
201.3 
202. 
202.7 

203.4 
204. 2 
204.9 
205.6 
206.3 

207.0 
207.8 
208.5 
209. 2 
2099 

210.6 

211. 3 
212.0 
212.8 
213- 5 

214.2 
2149 
2156 
216.4 


180.9 
181.7 
182.4 
183.2 
183.9 
184.7 

1854 
186. 2 
186.9 
187.7 
188.4 

189. 2 
189.9 
190.7 
I9I-4 
192.2 

192.9 
193-6 
194.4 
195- 1 
•95-9 

196.6 
197-4 
198. 1 
198.9 
199.6 

200. 4 

201. 1 

201. 9 

202. 6 
203.4 

204. 1 
204.9 

205. 6 
206.3 
207. 1 

207.8 
208.6 
2093 
2IO. 1 
210.8 

211.6 

212.3 
213- 1 

2.3.8 

214. 6 

215- 3 
216. 1 
216.8 
2175 
2.8.3 

219.0 
219.8 
220.5 
221.3 
222.0 

222.8 

223- 5 

224- 3 
225.O 


O 

1 
2 

3 
4 
5 

6 

7 
8 
9 
10 

11 

12 
'3 
«4 
15 

16 
17 
18 
19 

20 

21 

22 
23 
24 
25 

26 
27 
28 
29 
30 

31 
32 

33 
34 
35 

36 
37 
38 
39 
40 

4« 
42 
43 
44 
45 

46 
47 
48 
49 
50 

51 
52 
5. 

54 
55 

56 
57 
58 
59 


1391 


1491 


I590 


1689 


1789 


1888 


2087 


2186 


2286 


2385 


2484 


2584 


Horz. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .045 ft. to each 100 ft. of 
distance ior eacfc 10' departure. 



76 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 

5° 



500 



600 



700 



8.91 
8.94 
8.97 



9.14 
9.17 
9. 20 
9- 23 
9- 25 



9-34 
9-37 
9.40 

9-43 
9; 46 
9.48 
9- 5i 
9-54 



17-36 
17.42 



17.71 
17-77 
17.82 



18.22 

18.28 
1 8- 34 
18.39 
18.45 
18.51 

18.57 
18.62 
18.68 
18.74 
18.80 

18.85 
18.91 

18. 97 
19.02 
19.08 

19.14 

19. 20 
19- 25 
19-31 
"9-37 

19.42 
19.48 
19-54 
19. 60 
19.65 

19.71 

19- 77 
19.8! 



19.99 
20.05 
20. 11 
20. 16 
20. 22 

20.28 
20.34 
20.40 
20.45 
20. 51 

20.57 
20.63 
20.68 
20.74 



26.31 
26.39 
26.48 

26.56 
26.65 
26.73 
26.82 
26.90 

26.99 
27.08 
27. 16 
27-25 
27-33 

27.42 
27- 5» 
27-59 
27.68 
27.76 

27-85 
27-94 



28. 19 

28.28 
28.37 
28.. 45 
28.54 
28.62 



28.79 
28.88 
28.96 
29.05 

29- 13 
29. 22 
29- 3 1 
29- 39 
29.48 

29.56 
29.65 
29-73 
29.82 
29.90 



30.42 
30.50 
30-59 
30.68 
30.76 

30.84 
30.93 



34-7 
34-8 
35- o 
35- » 
35-2 
35-3 

35-4 
35-5 
35-6 



36.6 
36.7 
36.8 
36.9 



37-2 
37-4 
37-5 
37-6 

37-7 

37-8 
37-9 
38.0 
38.2 

38.3 
38.4 
38.5 
38.6 
38.7 

38.8 
39- o 



40.0 
40. 1 
40. 2 
40.3 
40.4 

40.6 
40.7 
40.8 
40.9 
41.0 



43-4 
43-6 
43-7 
43-8 
44.0 



44-3 
44.4 
44-5 
44-7 



45-3 
45-4 
45-6 

45-7 
45-8 
46.0 
46.1 
46.3 

46.4 
46.6 
46.7 
46.8 
47.0 

47.1 
47-3 
47-4 
47.6 
47-7 

47-8 
48.0 
48.1 
48.3 
48.4 

48.6 

48.7 



49-3 
49-4 
49.6 
49-7 
49.8 



52.3 
52.4 
52.6 
52.8 
53- o 



53-3 
53-5 
53-6 
53-8 

54- o 

54-2 
54-3 
54-5 
54-7 

54-8 
55- 
55-2 
55-3 
55-5 

55-7 
55-9 
56.0 
56.2 
56.4 

56.5 
56.7 
569 
57- i 
57-2 

57-4 
57-6 
57-8 
57-9 
58.1 

58.3 
58.5 
58.6 
58.8 
59- o 



59-3 
59-5 
59-6 
59-8 

60.0 
60. 2 
60.3 
60.5 
60.7 

60.8 
61.0 
61.2 



61.7 
61.9 
62.0 
62.2 



60.8 
61.0 
61.2 
61.4 
61.6 
61.8 

62.0 
62.2 
62.4 
62.6 
62.8 

63.0 
63.2 
634 
63.6 
63.8 

64.0 
64. 2 
64.4 
64.6 
64.8 

65.0 
65.2 
65- 4 
656 
65.8 



66.2 
66.4 



67.O 
67.2 
67.4 
67.6 
67.8 

68.O 
68.2 
68.4 
68.6 



69.0 
69.2 
69.4 
69.6 
69.8 

70.0 
70.2 
70.4 
70.6 
70.8 



72.0 
72.2 
72.4 
72.6 



72.4 
72.7 
72.9 



73-4 
73-6 
73-8 
74.0 

74-3 

74-5 
74-7 
75- o 

75-2 

75-4 
75-6 
75-9 
76.1 
76.3 

76.6 
76.8 
77.0 
77-2 
77-5 

77-7 
77-9 
78.2 
78.4 
78.6 

78.8 
79.1 
79-3 
79-5 



Hon dist. Is for 30' point. Add or subtract .055 ft. to each 100 ft. of 

distance for each 10' deoarture. __ ._ „ 



TOPOGRAPHIC STADIA SURVEYING 



77 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
5° 



1400 


1500 


1600 


1700 


1800 


1900 


2100 


2200 


2300 


2400 


2500 


2600 


f 


121. 6 
122. O 
122.4 
122.8 
123.2 
123.6 

I24.O 
I24.4 
124.8 
125.2 
125.6 

126.0 
I26.4 
126.8 
127.2 
127.6 

127.0 
I28.4 
128.8 
129. 2 
I29.6 

I30.0 
I3O.4 
I3O.8 
I3>-2 

1)1.6 

132.0 
«32-4 
132-8 
133- 2 
133-6 

'34- 
134- 4 
134-8 
135 2 
"35-6 

136.0 
1364 
136.8 
137-2 
137.6 

138.0 
138.4 
138.8 
»39-2 
139-6 

140.0 
140.4 
140.8 
141. 2 
141. 6 

142.0 
142.4 
142.8 
143-2 
143-6 

«43-9 
144-3 
144.8 
'45- 1 


130.2 
I30-7 
13'- 1 
I3I-S 
1320 
132- 4 

1328 
133-2 
133-7 
134- 1 
134-5 

135- 
135-4 
135-8 
136.2 
136.7 

137- 1 
137.5 
138.0 
138- 4 
1388 

139-3 
139-7 
140. 1 
140.5 
141. 

141.4 
141.9 
1423 
142.7 
143- 1 

143.6 
144.0 
144.4 
144- 8 
145- 3 

145- 7 
146. 1 
146.5 
147.0 
147-4 

147.8 
148.2 
148.7 
149. I 
149-5 

150.0 
'504 
150.8 
151- 2 
151-- 7 

1521 

"52-5 
1529 
«53- 4 
153- 8 

154- 2 
"54-6 
155- > 
•55-5 


1389 
139- 4 
139- 8 
140.3 
140.8 

141. 2 

141.7 

142. I 
142.6 
143.O 

143- 5 

144.0 

144.4 
144.9 
•45-3 
145.8 

146. 2 
146.7 
1472 
147.6 
148. I 

148.5 
149.0 
149.4 
'59-9 
150.4 

1509 
«5>-3 
151-7 
152.2 
152.6 

153- 1 

153-6 
i54-o 
154- 5 
155- 

•55- 4 
155-8 
156.3 
156.8 
157- 2 

1577 
158. 1 
158.6 
159- 
159-5 

160.0 
160.4 
160.9 
161.3 
161. 8 

162.2 
162.7 

163. 1 
163.6 

164. 1 

164.5 
165.0 
165- 4 
165 9 


147.6 

148. 1 
148.6 

149. 1 
149- 5 
150.0 

150.5 
151.0 
I5I-5 
1520 
1525 

153-0 

153- 4 
153- 9 
154-4 
154- 9 

155- 4 
155-9 
156.4 
156.8 
1573 

157- 8 
158.3 
158.8 
159- 3 
159-8 

160.2 
160.7 
161. 2 
161. 7 
162.3 

162.7 
163.2 
163.6 

164. 1 
164.6 

165. 1 
165.6 

166. 1 
166.6 
167.0 

167- 5 
168.0 
168.5 
169.0 
1695 

169.9 
170.4 
170.9 
171.4 
I7I-9 

172.4 
172.9 
•73- 3 
173- 8 
174- 3 

174- 8 
•75- 3 
175-8 
176.2 


156- 3 
156.8 
157-3 
157-8 
158.3 
158.8 

159- 4 
159- 9 
160.4 
160. 9 

161. 4 

162.0 
162.5 
163.0 
163.5 
1640 

164.5 
1650 
1656 

166. 1 
166.6 

167. 1 
167.6 

168. 1 
168.6 

169. 2 

169.7 

170. 2 
I70.7 
171. 2 
171.7 

172.2 
172.8 

173-3 
173-8 
174-3 

174.8 
175-3 
175 8 
176.4 
176.9 

177- 4 
178.9 
178.4 
178 9 
179- 4 

179-9 
180.5 
181 

181. 5 
182.0 

.82.5 
183.0 
183.5 
184.0 
184.6 

185. I 
185.6 

186. 1 
186.6 


165.0 
165.5 
166.0 
166.6 
1671 
1677 

168.2 
168.8 
169.3 
169.9 
170.4 

i 7 r.o 

1715 
172.0 
172.6 
173- 1 

173- 7 
1742 
174.8 
•75- 3 
175-8 

176.4 
176 9 
177-5 
178.0 
178.6 

179 I 

179-7 
180.2 
180.7 
181.3 

181.8 
182.4 

182 9 

183 4 
184.0 

1845 
185.1 

185 6 

186 2 
186.7 

187.2 

187 8 
188.3 
189.9 
189.4 

1899 
190.5 
191. 
191. 6 
192.0 

192.7 
193-2 
193- 7 
194-3 
194- 8 

195- 4 
195- 9 
196.4 
197.0 


182.3 
182.9 
183- 5 
184. 1 
184.7 
1853 

185.9 
186.5 
187.1 
187.7 
188.3 

188.9 
1895 
190. 1 
190.7 
191.4 

192.0 
1925 
193- 1 
•93- 7 
•94- 3 

195.0 
195- 6 
196. 2 
196.7 
•97- 3 

197- 9 
198.6 
199.2 
199.7 
200.3 

200. 9 
201 5 
202. 1 
202.7 
203.3 

203.9 
204.5 
205. 1 
205.7 
206.3 

206.9 
207 5 
208. 1 
208.7 
209.3 

209.9 
210.5 
211. 2 
211. 7 
212.4 

212.9 
213- 5 
214.1 
214.7 
215.3 

215-9 
216.5 
217. 1 
217.7 


191.0 
191. 6 
192.3 
1929 
•93- 5 
194.2 

194.8 
195- 4 
196.0 
1967 
197- 3 

1979 
198.6 
1992 
1 99- 8 
200.5 

201. 1 
201.7 

202.3 
203.0 
203.6 

204. 2 
204.9 

205- 5 
206. 1 
206.7 

207.4 
268.0 
208.6 
209.3 
209.9 

210.5 
211. 1 
211. 8 
212.4 
213.0 

2137 

214- 3 
214.9 

215-5 
216. 2 

216.8 
217.4 
218 
218.7 
219- 3 

219.9 
220.6 
221.2 
221.8 
222.4 

223- 1 

223.7 
224.3 
225.0 
225. 6 

226.2 
226.8 
227.4 
228.1 


200.0 

201. 7 
202.3 
203.0 

203.6 
2043 
205.0 
205.6 
206.3 

206.9 

207. 6 
208.3 

208. 9 
209.6 

2IO. 2 

2IO. 9 
2115 
212. 2 
212.8 

213- 5 
214.2 
214.8 
215-5 
216. I 

216.8 
217-5 
2l8. I 
218.8 
219.4 

220. I 
2 20. 7 
221.4 
222. 1 
222.7 

223.4 
224.O 
224.7 
225.3 
226.0 

226.7 
227.3 
227.9 
228.6 
2293 
229.9 

230. 6 
231.2 
231-9 
232.6 

233- 2 

233- 9 
234- 5 
235- 2 
235- 8 

2365 
237- 1 
237-8 
2384 


208.4 
209. 1 
2097 
210.5 
211. 1 
211. 8 

212.5 
2132 
2139 
214.6 
2152 

2159 
216.6 
2173 
218.0 
218.7 

219-4 
220. 1 
220. 7 
221.4 
222. 1 

222.8 

2235 
224.2 
224.9 

225- 5 

226. 2 

226. 9 

227. 6 

228.3 

229.0 

229.7 
230.3 
231.0 
2317 
232.4 

233. 1 

233-8 
234- 5 
235- 1 
235- 8 

236.5 

237 2 
237 9 
2386 
239- 2 

239- 9 
240. 6 
241-3 
242.0 
242.7 

243-3 
244.0 
244.7 
245-4 
246. 1 

246.8 
247- 4 
248. 1 
248.8 


217.1 
217.8 
218.5 
219.2 
219.9 
220.6 

221.4 
222. 1 
222.8 

2235 
224.2 

2249 
225.6 

226. 4 

227. 1 
227.8 

228.5 
229.2 
2299 
2307 
2314 

232.1 

232.8 
233- 5 

234-2 

234-9 

235- 6 
236.4 
237- 1 
237-8 
238-5 

239-2 

239-9 
240. 6 
241.4 
242.1 

242.8 
243-5 
244.2 
244.9 
245-6 

246.4 
247.1 
2478 
2485 
249.2 

249.9 
250.6 
251 4 
252.1 

252.8 

253- 5 

254-2 

254- 9 
255-6 
256.3 

257.0 
257 8 
258.5 
259-2 


2257 
226.5 
227.2 
228.0 
228.7 

229- 5 

230.2 
2310 
231-7 
232.4 
233-2 

233- 9 
234- 7 
235-4 
236.2 
236 9 

2377 
238.4 
239- 1 
239 9 
240.6 

241.4 
242. 1 
2429 
243.6 
244- 3 

245- 1 
2458 
246. 6 
247- 3 
248.0 

248.8 
249- 5 
250.3 
251.0 
251.8 

252 5 
253- 3 
254- 
254- 7 
255- 5 

2562 
257 
257- 7 
258.4 
259.2 

259- 9 

260. 7 

261. 4 

262. 1 
262.9 

263.6 
264.4 
265. 1 
265.8 
266.6 

2673 
268.1 

268.8 
2695 




2 
3 
4 
5 

6 
7 
8 
9 
10 

11 
12 
13 
14 
15 

16 
17 
18 
19 

20 

21 

23 
24 
25 

26 
27 
28 
29 
30 

3« 

32 
33 
34 
35 

36 

37 
38 
39 
40 

41 

42 
43 
44 
45 

46 
47 
48 
49 
SO 

51 
52 
53 
54 
55 

56 
57 
58 
59 


1387 


i486 


1585 


1684 


1783 


1882 


2081 


2180 


2279 


2378 


2477 


2576 


Horz. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .055 ft. to each 100 ft. of 
distance for each 10' departure. 



78 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
6° 



f 100 200 3Q0 400 500 600 700 



900 1100 1200 1300 



21.47 
2t-53 
21-59 
21.64 

21.70 
21. 76 
21.81 
21.87 
21.93 

21.98 
22.04 



22. 27 
22.33 
22.38 



23.12 

23. 18 
23- 23 
23.29 
23- 34 

23.40 
23.46 
23-5' 
23-57 
23- 63 

23.68 
23-74 
23.80 
23- 85 
23-9' 

23- 97 
24.02 
24.08 

24. 14 



3'- 19 
31- 27 
3'- 36 

3'-44 
3»-53 
31.61 

31.69 
3«-78 



32- 04 

32.12 
32.21 
32.30 
32.38 
32.47 

32.55 
32.64 
3272 
32.81 
32.89 

32.98 
33-o6 



33- 40 
33-49 
33-57 
33-66 
33-74 

33- 83 
33-91 
34.00 
34.08 
34-17 

34- 25 
34-34 
34-42 
34-51 
34-59 

34-68 
34-76 
3484 
34-93 
35- 02 

35- 10 
35- 19 
35-27 
35- 36 
35-44 

35-53 
35.6i 
35- 7o 
35- 78 
35-86 

35-95 
36.03 
36.12 
36.20 



41.6 

4i-7 
41.8 
41.9 
42.0 
42.2 

42.3 
42-4 
42.5 
42.6 
42.7 

42.8 
42.9 
43- 1 
43-2 
43-3 

43-4 
43-5 
43-6 
43-7 
43-9 



45- 1 
45-2 
45-3 
45-4 
45-6 

45-7 
45-8 
45-9 
46.0 
46. 1 

46. 2 
46.4 
46.5 
46.6 
46.7 

46.8 
46.9 
47.O 



47-4 
47-5 
47.6 
47-7 
47.8 

47-9 
48.0 
48.2 
48.3 



52.0 
52- 1 
52.3 
52-4 
52.5 
52-7 

52.8 
53- o 
53- 1 
53-3 
53-4 

53-5 
53-7 
53-8 
54- o 
54-1 

54-2 
54-4 
54-5 
54-7 
54-8 



55-2 
55-4 
55-5 

55-7 
55-8 
56.0 
56.1 
56.2 

56.4 
56.5 
56.7 
56.8 
56.9 



57-2 
57-4 
57-5 
57-6 

57.8 
57-9 
58.1 
58.2 
58.4 



58.6 
58.8 
58.9 



59-4 
59-5 
59-6 
59-8 



62.4 
62.5 
62.7 
62.9 
63.1 
63.2 

63.4 
63.6 
63.7 
63- 9 
64.1 

64.3 

64.4 
64.6 
64.8 
64.9 

65.1 
65- 3 
65- 4 
65.6 
65.8 

66.O 
66.1 
66.3 
66.5 
66.6 

66.8 
67.0 
67.1 
67- 3 
67.5 

67.7 
67.8 
68.0 
68.2 
68.3 



68.7 
68.8 
69.0 
69. 2 

S 4 

69- 5 
69.7 
69.9 
70.0 

70.2 
70.4 
70.5 
70.7 
70.9 

71.0 
71.2 
71.4 



71.9 
72. 1 
72.2 
72.4 



83. 

83. 

83. 

83. 

84.1 

84-3 

84.5 
84.8 
85.0 
85.2 
85-4 

85.7 
85- 9 



1150 
"5-3 
115.6 



118.4 

1 18. 7 

119. o 

1 19. 4 
119-7 
120.0 
120.3 
120.6 

120.9 



124.0 
124-3 
124.7 
125.0 
125- 3 
125.6 

1 25- 9 
126.2 
126.5 
126.8 

127.1 
127.5 
127.8 

128. 1 
128.4 

128.7 

129. o 
129.3 
129.6 
129.9 

130.3 
130.6 
130.9 



132. 1 
132.4 
132.7 



124.7 

125. 1 
J 25. 4 
125.8 

126. I 
126.5 

126.8 

127. I 
127-5 
127.8 
128.2 



129.2 

1295 
129.9 

1302 
130.5 
J 30. 9 



132. 2 
132.6 
132.9 

133- 3 

133- 6 

134- o 
» 34- 3 
134-6 

135- o 

»35-3 
135-6 
136.0 
136.3 
136.7 

I37.0 
"37-4 
137-7 
138.0 
138.4 

138.7 

139.0 
139- 4 
'39-7 
140. 1 



142. 1 
142.4 
142.8 
'43-1 
'43-5 

'43-8 



Hor. dist. is for 30' point. Add or subtract .065 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



79 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 

7° 



100 200 300 



500 600 700 800 900 1100 1200 1300 



12.24 

12.27 
12.29 
12.32 
12-35 
12.38 

12.41 
12.43 
12.46 
12.49 
12.52 

12-55 
12.58 
12.60 
12.63 
12.66 

12.69 
12.72 
12.74 
12.77 
12.80 



12.97 
13.00 
13.02 
13- 05 
13-08 

13 11 
13- 14 
13- 17 
13.20 
13- 22 

13- 25 
13.28 
13-31 
«3-33 
13- 36 

13-39 
13- 42 
13-45 
13-47 
13- 50 

13-53 
13- 56 
13- 59 
1361 
13- 64 

13- 67 
1 3- 70 
•3-73 
13-75 



24.19 
24- 25 
24.30 
24- 36 
24.42 
24-47 

24-53 
24-59 
24.64 
24.70 
24.76 

24.81 
24.87 
24.92 
24.98 
25- 04 

25- 09 



25. 26 
25- 32 

25- 38 
25-43 
25-49 
25-54 
25.60 

2566 
25-7' 
25-77 
25- 83 
25.88 

25- 94 
25-99 
26.05 

26. fi 



26.28 
26.33 
26.40 
26.44 

26.50 
26.56 
26.61 
26.67 
26.72 

26.78 
26.84 
26.89 
26.94 
27.00 

^7.06 



27. 23 - 
27.28 

27-34 
27.40 
27-45 
27- 51 



36.29 
36.37 
36.46 
36.54 
36.63 
36.71 

36.80 
36.88 
36.97 
37- 05 
37- 1,3 

3722 
37- 30 
37-39 
37-47 
37- 56 

37-64 
37-73 



37- 98 

38.06 
38.15 
38.23 
38.32 
38.40 

38.49 
38.57 
38.65 
38.74 
38.82 

38.91 
38.99 
39.08 
39- 16 
39-24 

39-33 
39-41 
39- 50 
39.60 
39.66 

39-75 
39- 83 
39-92 
40.00 
40.09 

40.17 

40.25 
40.34 
40.42 
40.50 

40.59 
40.67 
40.76 
40.84 
4093 

41.01 
41.09 
41. 18 
41. 26 



49.2 
49-3 
49-4 
49-5 

49-6 
49-7 
49.8 
50.0 
50.I 

50.2 
50.3 
50.4 
50.5 
50.6 

50.8 
509 
51.0 
5«-i 
5'-2 



52.4 
52.6 
52.7 
52.8 
52.9 

53- o 
53- 1 
53-2 
53-3 
53-4 

53-6 
53-7 
53-8 
53-9 
54- o 



54-2 
54-3 
54-5 
54-6 

54-7 
54-8 
54-9 
55- o 



61.3 
61.5 
61.6 
61.8 
61.9 

62.0 
62.2 
62.3 
62.5 
62.6 

62.7 
62.9 
63.0 
63.2 
63- 3 

63- 4 
636 
63.7 
63- 9 
64.0 

64. t 
64- 3 
64.4 
64.6 
64.7 

64.8 
65.0 
65.1 
65- 3 
65- 4 

65- 5 
65- 7 
65.8 
66.0 
66.1 

66.2 

66.4 
66.5 
66.7 
66.8 

67.0 
67.1 
67.2 
67.4 
67.5 

67.7 
67.8 
67.9 



68.5 
68.6 
68.8 



89. 2 
89.4 
89.6 

90.0 
90.0 

90. 2 
90.4 
90.6 



91.2 
91.4 
91.6 



92.2 
92.4 
92.6 

92.8 
92.9 



95-7 
95-9 
96.1 
96.3 



133- 1 
133-4 
133-7 
134.0 
134-3 
134.6 

134- 9 
135- 2 
•35- 5 



136.5 
136.8 



138.0 
138.3 
138.6 
138.9 
139- 3 

139- 6 
139- 9 
140. 2 
1405 
140.8 

141. 1 
I4I-4 
Hi-7 
142.0 
142.4 

»42. 7 
143- o 
143- 3 
143.6 
H3-9 

144.2 
144-5 
144.8 
145-2 
145-4 

145-8 
146. 1 
146.4 
146.7 
147.0 

147. 2 
147.6 
147-9 
148.2 
148.6 

148.8 
149. 1 
149.4 
149.8 
150. x 

150.4 
150.7 
151 
151-3 



145- 2 
145-5 
145-8 
146.2 
146.5 
146.8 

147.2 
147-5 
147- 9 
148.2 
148.6 

148.9 
149.2 
149.6 
149.9 
150. 2 

150.6 
1 50- 9 
151-2 

151. 6 
151-9 

1523 
152.6 
1529 
153- 3 
153-6 

153-9 
154-3 
154-6 
155- o 
155-3 

155- 6 
156.0 
1563 
1566 
J57-0 

157- 3 
157.6 
158.0 
158. 4 
158.7 

1590 
159- 3 
159- 7 
^60.0 
160.3 

160.6 
161. o 
161. 4 

161. 7 
162.0 

162.4 
162.7 
163.0 
163-4 
163-7 

164.0 
164.4 
164.7 
165.0 



98.29 



1081 



1 179 



Hor. dist. is for 30' point. Add or subtract .075 ft. to each 100 ft. of 
distance for each 10' departure* 



80 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
8° 



t ' 


100 


200 


300 


400 


500 


600 


700 


800 


900 


1100 


t 


o 


13-78 


27-56 


4i. 35 


55- 1 


68.9 


82.7 


96.5 


1 10. 3 


124.0 


151. 6 





I 


13-81 


27.62 


41- 43 


55-2 


69.0 


82.9 


96.7 


no. 5 


124- 3 


151-9 


1 


2 


13- 84 


27.68 


41-51. 


55-4 


69. 2 


83.0 


96.9 


no. 7 


124- 5 


152.2 


2 


3 


13- 87 


27-73 


41.60 


55-5 


69- 3 


83.2 


97.1 


1 10.9 


124.8 


152- 5 


3 


4 


13.89 


27.78 


41.68 


55-6 


69- 5 


83-4 


97-3 


in. 2 


125.0 


152.8 


4 


5 


I3.92 


27.84 


41.76 


55-7 


69.6 


83.5 


97-4 


in. 4 


125- 3 


153- 1 


5 


6 


»3-95 


27.90 


41.85 


55-8 


69.8 


83.7 


97.6 


in. 6 


125.6 


153- 4 


6. 


7 


13.98 


27.96 


41- 93 


55-9 


69.9 


83- 9 


97-8 


in. 8 


125.8 


153- 8 


7 


8_ 


14.01 


28.01 


42.02 


56.0 


70.0 


84.0 


98.0 


112. 


126.0 


154- 1 


8 


9 


14.03 


28.07 


42. IO 


56.1 


70.2 


84.2 


98.2 


112.3 


126.3 


154- 4 


9 


IO 


14.06 


28.12 


42.18 


56.2 


70.3 


■84.4 


98.4 


112.5 


126.6 


154- 7 


10 


Ii 


14.09 


28.18 


42. 27 


56.4 


70.4 


84-5 


98.6 


112.7 


126.8 


155-0 


11 


12 


1412 


28.23 


42.35 


56.5 


70.6 


84.7 


98.8 


112.9 


127.0 


155- 3 


12 


13 


14. 14 


28.29 


42.44 


56.6 


70.7 


84.9 


99.0 


1 13- 2 


127- 3 


155- 6 


13 


14 


14- '7 


28.35 


42.52 


56.7 


70.9 


85.0 


99.2 


1 13- 4 


127.6 


155- 9 


14 


'5 


14. 20 


28.40 


42. 60 


56.8 


71.0 


85.2 


99-4 


1 13. 6 


127.8 


156.2 


15 


i6- 


14-23 


28.46 


42.68 


56-9 


71-1 


85-4 


99.6 


113. 8 


128.0 


156.5 


16 


17 


14. 26 


28.51 


42.77 


57-0 


71-3 


85.5 


99-8 


1 14.0 


128.3 


156.8 


>7 


18 


14.28 


28.57 


42.85 


57- 1 


7i-4 


85.7 


100. 


1 14- 3 


128.6 


157-1 


18 


»9 


14-31 


28.62 


42.94 


57-2 


71.6 


85- 9 


100.2 


114- 5 


128.8 


157- 4 


19 


20 


14-34 


28.68 


43- 02 


57-4 


71.7 


86.0 


100.4 


1 14. 7 


129. 1 


157- 7 


20 


21 


14- 37 


28.74 


43- 10 


57-5 


71.8 


86.2 


100.6 


114. 9 


"9.3 


1580 


21 


22 


14.40 


28.79 


43- 19 


57-6 


72.0 


86.4 


100.8 


II5-2 


129.6 


158.4 


22 


23 


14.42 


28.95 


43-27 


57-7 


72. 1 


86.5 


101.0 


1 15- 4 


129.8 


158.7 


23 


24 


14-45 


28.90 


43- 36 


57-8 


72.3 


86.7 


101.2 


1 15. 6 


130. 1 


159- 


24 


25 


14.48 


29.96 


43-44 


57-9 


72.4 


86.9 


101.4 


115.8 


130.3 


159- 3 


25 


26 


14-51 


29.02 


43-52 


58.0 


72.5 


87.0 


101.6 


116. 1 


130.6 


159- 6 


26 


27 


14-54 


29.07 


43-6o 


58.1 


72.7 


87.2 


101.7 


1 16..3 


130.8 


159- 9 


27 


28 


14. 56 


29- 13 


43- 69 


58.2 


72.8 


87.4 


101.9 


116.5 


1311 


160. 2 


28 


29 


14-59 


29. 18 


43-77 


58.4 


73- 


87.6 


102. 1 


1 16. 7 


131-3 


160.5 


29 


30 


14.62 


29.24 


43- 85 


58.5 


. 73- 1 


87.7 


102.3 


1 16. 9 


1316 


160.8 


30 


31 


14- 65 


29.29 


43-94 


58.6 


73-2 


87.9 


102.5 


117. 2 


1318 


161. 1 


3i 


32 


14.67 


29-35 


44.02 


58.7 


73-4 


88.0 


102.7 


1 17. 4 


132. 1 


161. 4 


32 


33 


14.70 


29.40 


44.11 


58.8 


73-5 


88.2 


102.9 


1 17. 6 


^32.3 


161.7 


33 


34 


14-73 


29.46 


44.19 


58.9 


73-6 


88.4 


103.1 


1 17. 8 


132.6 


162.0 


34 


35 


14.76 


29.52 


44-27 


59- 


73-8 


88.6 


103.3 


118. 1 


132.8 


162.3 


35 


36 


14- 79 


29- 57 


44- 36 


59- 1 


73-9 


88.7 


103.5 


1 18. 3 


133. 1 


162.6 


36 


37 


14.81 


29.63 


44-44 


59-2 


74. 1 


88.9 


1037 


118.5 


133-3 


162. 9 


37 


38 


14.84 


29.68 


44-52 


59-4 


74.2 


89.0 


1039 


118.7 


133-6 


163.2 


38 


39 


14.87 


29-74 


44.61 


59-5 


74-3 


89.2 


104. 1 


1 19.0 


133-8 


163.6 


39 


40 


14.90 


29.78 


44.69 


596 


74-5 


89.4 


104.3 


119. 2 


134- 1 


163- 9 


40 


4i 


14.92 


29-85 


44-77 


59-7 


74.6 


89.6 


104.5 


1 19. 4 


134- 3 


164. 2 


4i 


42 


14-95 


29.90 


44.86 


59-8 


74.8 


89.7 


104.7 


1 19. 6 


134.6 


164.5 


42 


43 


14.98 


29.96 


44-94 


59-9 


74-9 


89.9 


104.9 


1 19. 8 


134.8 


164.8 


43 


44 


15.01 


30.02 


45.02 


60.0 


75- 


90.0 


105.0 


120. 1 


135.1 


165. 1 


44 


45 


15-04 


30.07 


45- 11 


60.1 


75-2 


90.2 


105.2 


120.3 


135- 3 


165- 4 


45 


46 


15- 06 


30- 13 


45-18 


60.2 


75-3 


90.4 


1054 


120.5 


135- 6 


165- 7 


46 


47 


15.09 


30. 18 


45-27 


60.4 


75-5 


90. 6 


105. 6 


120.7 


135-8 


166.0 


47 


48 


15- 12 


30.24 


45-36 


60.5 


75-6 


90.7 


105. 8 


121. 


136. 1 


166.3 


48 


49 


15- 15 


30.29 


45-44 


60.6 


75-7 


90.9 


106.0 


121. 2 


136.3 


166.6 


49 


50 


15- 17 


30-35 


45-52 


60.7 


75-9 


91.0 


106.2 


121. 4 


136.6 


166.9 


SO 


-51 


15- 20 


30.40 


45- 60 


60.8 


76.0 


91.2 


106.4 


121.6 


136.8 


167.2 


51 


52 


15- 23 


30.46 


45- 69 


60.9 


76.2 


91.4 


106.6 


121. 8 


137- 1 


1675 


52 


53 


1526 


30.51 


45-77 


61.0 


76.3 


91- 5 


106.8 


122. 1 


137-3 


167.8 


53 


54 


15.28 


30.57 


45-86 


61.1 


76.4 


91.7 


107.0 


122.3 


137.6 


168. 1 


54 


55 


15- 31 


30.62 


45-94 


61.2 


76.6 


91.9 


107.2 


122.5 


137.8 


168.4 


55 


56 


15-34 


30.68 


46.02 


61.4 


76.7 


92.0 


107.4 


122.7 


138.1 


168.7 


56 


57 


15-37 


3074 


46. IO 


61.5 


76.8 


92.2 


107.6 


122.9 


138.3 


169.0 


57 


58 


15- 40 


3079 


46. 19 


61.6 


77.0 


92.4 


107.8 


123.2 


138.6 


169.4 


58 


59 


15- 42 


30.85 


46.27 


61.7 


77- 1 


92-5 


108.0 


123-4 


138.8 


169.6 


59 


Horz. 
Dist. 


9782 


195- 6 


293-5 


391- 3 


489-1 


587 


685 


783 


880 


1076 


Hon. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .085 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



81 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
9° 



33- 98 
34- 04 
34- 09 
34- 16 



46.35 
46.44 
46.52 
46.60 
46.68 
46.77 

46.85 
46.93 
47.02 
47.10 
47.18 

47.26 
47-35 
47-43 
47-51 
47.60 

47.68 
47.76 
47.84 
47-93 
48.01 

48.09 
48.17 
48.26 
48.34 
48.42 

48.51 
48.59 
48.67 
48.75 
48.84 

48.92 
49.00 
49.08 
49- 17 
49-25 

49-33 
49.41 
49- 5o 
49- 58 
49.66 

49-74 
49.82 
49.91 
50.00 
50.07 

50. 15 
5024 
50.32 
50.40 
50.«48 

5056 
5065 
50.73 
50.81. 
50.89 

50.98 



61.8 
61.9 
62.0 
62.1 
62.2 
62.4 

62.5 
62.6 
62.7 
62.8 
62.9 

63.0 
«3-i 
63.2 
63- 4 
63- 5 

63.6 

63- 7 
63.8 

63- 9 
64.0 

64. 1 
64.2 
64-3 
64.4 
64.6 

64.7 
64.8 
64.9 
65.0 
65-1 

65.2 
65-3 
65- 4 
65.6 
65- 7 

65*. 8 
65- 9 
66.0 



66.3 
66.4 
66.5 
66.6 
66.8 

66.9 
67.0 
67.1 
67.2 
67.3 

67.4 
67-5 
67.6 
67.8 
67.9 



93-2 
93-4 
93-5 

93-7 
93-9 
94.0 



94-5 
94-7 
•94-9 



95-4 
95-5 
95-7 
95-8 
96.0 

96.2 
964 
96.5 
96.7 
96.8 



97-3 
97-5 
97-7 

97-8 
98.0 



99.0 
99-2 
99-3 

99-5 
996 
99.8 
00.0 



108.4 


123- 
"3- 


108.5 


124. 


108.7 


124. 


108.9 


124. 


109. 1 


124. 


109.3 


124. 


1095 


«25- 


109.7 


»25- 


109.9 


>25- 


1 10.. I 


>25- 


no. 3 


126. 


1 10. 5 


126. 


1 10. 7 


126. 


1 10. 9 


126. 


in. i- 


126. 


in. 2 


127. 


in. 4 


127. 


in. 6 


127. 


111,8 


127. 


112. 


128. 


112.2 


128. 


112.4 


128. 


112.6 


128. 


112.8 


128. 


1130 


129. 


"3-2 


129. 


II3-4 


129. 


U3-6 


129. 


113.8 


130. 


114. 


130. 


114. 1 


130. 


"4-3 


130. 


114- 5 


130. 


1 14. 7 


I3>- 


1 14. 9 


I3i- 


M5- 1 


>3i- 


"5-3 


Mi- 


i'5-5 


132. 


"5-7 


132. 


i'5-9 


132. 


116. 1 


132. 


1 16. 3 


132. 


116. 4 


133- 


116.6 


133- 


116.8 


133- 


117.0 


133- 


117. 2 


•34- 


1 17. 4 


«34- 


1 17. 6 


134- 


1 17. 8 


134- 


1 18.0 


134. 


118.2 


'35- 


118.4 


»35-. 


1 18. 6 


'35- 


118. 8 


135- ' 


118. 9 


135- ! 


119. 1 


136.: 


119- 3 


136. < 


119- 5 


136. t 



>39' 
139- 3 
139- 6 



140.6 
140.8 
141. o 
I4I-3 
<4i-5 

141. 8 
142.0 
1423 
>42- 5 
142.8 

143- o 
143-3 
«43-5 
1438 



144-3 
144-5 
144.8 
•45- o 
»45-3 

•45-5 
145-8 
146.0 
•46-3 
1465 

146.8 
147.0 
147.2 
147-5 
>47-7 

148.0 
148. 2 
148.5 
148.7 
149.0 

149.2 
149-5 
«49-7 
150.0 
150.2 



152.2 
152.4 
I52-7 

1529 
>53-2 
»53-4 
153-7 



194.6 



Horz. 
Dist^ 



Hor. dist. is for 30' point. Add or subtract .095 ft. to each 100 ft. of 
distance for each io 7 departure. 



82 



TOPOGRAPHIC STADIA SURVEYING 



Horz. 
T)ist. 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
10° 



100 200 300 400 500 600 700 800 900 1100 



34- 20 
34.26 
34- 31 
34-37 
34-42 
34- 48 

34-53 
34- 58 
34- 64 

34- 69 
34-75 

34.80 
34.86 
34-91 
34-97 

35- 02 

35- 08 
35- »3 
35- 18 
35-24 
35-29 

35-35 
35- 40 
35- 46 
35- 5i 
35- 56 

35-62 
35- 67 
35-73 
35- 78 
35- 84 

35- 89 
35-94 
36.00 
36.05 
36.11 

36.16 
36.22 
36.27 
36.32 
36.38 

36.43 
36.49 
36.54 
36.60 
3665 

3670 
36.76 
36.81 
36.87 
36.92 

36.98 
37- 03 
37.08 
37- 14 
37- 19 

37-24 
37- 30 
37-35 
37- 4i 



193- 4 



1064 Horz. 
J Dist. 



Hor. dist. is for 30' point. Add or subtract .105 ft. to each ioo ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA. SURVEYING 



S3 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
11° 



100 200 300 400 500 600 700 800 900 1100 



9.19 
9.22 
9.24 
9.27 

9- 30 
9-32 
9-35 
9-38 
9.40 

9-43 
9.46 
9.48 
9- 5i 
9-54 

9-56 
9-59 
9. 62 
9.64 
9.67 

9.70 
9.72 
9-75 
9.78 
9. 80 

9-83 
9.86 
9.88 
9.91 
9-94 

9.96 
9-99 
20.02 
20.04 
20.07 



20. 20 

20.23 
20. 26 
20.28 
20.31 



96.03 



37- 46 
37-52 
37-57 
37-62 
37.68 
37-73 

37-78 
37-84 
37- 89 
37-95 
38.00 

38- 05 
38.11 
38.16 
38.22 
38.27 

38.32 
38.38 
38.43 
38.48 
38.54 

38.59 
38.64 
38.70 
38.75 
38.80 

38.86 
38.91 
38.97 
39.02 
39- 07 

39- 13 
39- 18 
39- 23 
39- 29 
39-34 

39-39 
39-45 
39- 50 
39- 56 
39.61 

39.66 
39-72 
39-77 
39-82 
39-88 

39-93 



40. 14 

40. 20 
40.25 
40.30 
40.36 
40.41 

40.46 
40.51 
40.57 
40. 62 



192. 



56. 19 
56.27 
56.36 
56.43 
56.51 
56.60 

56.68 
56.76 
56.84 
56.92 
57- 00 

57- 08 
57- 16 
57-24 
57- 32 
57-40 

57-48 
57- 56 
57.64 
57- 72 
57.8i 

57.89 
57-97 
58.05 
58.13 
58.21 

58.29 
58.37 
58.45 
58.53 
58.61 

58.69 
58.77 
58.85 
58.93 
59- 01 

59- 09 
59- '7 
59-25 
59-33 
59- 4« 

59-49 
59-57 
59- 65 
59-73 
59-8i 

59- 89 
59-97 
60.05 
60. 13 
60. 21 

60. 29 
60.37 
60.45 
60.53 
60.61 

60. 69 
60.77 
60.85 
60.93 



2S8. 



75-2 
75-4 
75-5 

75-6 
75-7 
75-8 
75-9 
76.0 

76.1 
76.2 
763 
76.4 
7^5 

76.6 
76.8 
76.9 
77.0 
77.1 

77.2 
77-3 
77-4 
77-5 
77-6 



77-9 
78.0 
7 8.2 

78.2 
78.4 
78.5 
78.6 
78.7 

78.8 
78.9 
79.0 
79.1 
79.2 

79-3 
79-4 
79-5 
79.6 



80.1 
80.2 
80.3 



80.6 
80.7 
80.8 



768 



Hor. dist. is for 30' point. Add or subtract .113 ft. to each 100 ft. of 
distance for each 10' departure. 



84 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
12° 



600 



700 



40.67 
40.73 
40.78 
40.83 
40.89 
40.94 

40.99 
41.04 
41. 10 
41-15 
41. 20 

41.26 
41-31 
4i- 36 
41.42 
41.47 

4i- 52 
41.58 
41.63 
41.68 
41-73 

41.79 
41.84 
41.89 
41.94 
42.00 

42.05 



42-32 
42-37 
42.42 
42.47 
42.52 

42- 58 
42.63 
42.68 
42- 74 
42.79 

42.84 



43-21 
43-26 
43-31 

43-37 
43-42 
43-47 
43-52 
43-58 

43- 63 
43-68 
43-73 
43-78 



61. 01 
61.09 
61.17 
61.25 
6i-33 
61. 41 

61.49 
61.57 
61.65 
6i.73 
61.81 

61.89 
61.97 
62.04 
62. 12 
62.20 

62.28 
62.36 
62.44 
62.52 
62.60 

62.68 
62.76 
62.84 
62.92 
63.00 

63.08 
63.16 
63- 23 
63- 3i 
63- 39 

63-47 
63- 55 
63.63 
63- 7i 
63- 79 

63.87 
63- 95 
64.02 
64. 10 

64. 18 

64.26 
64-34 
64.42 
64.50 
64.58 

64.66 
64- 73 
64.81 
64.89 
64.97 

65- 05 
65- 13 
65.21 
65.28 
6536 

65-44 
65- 52 
65.60 

65. 68 



101.7 
101.8 
102.0 



102.9 
103.0 

103. 1 

103-3 
.103. 4 
103.5 
103.7 

103.8 
103.9 
104.1 

104. 2 
104.3 

104.5 
104.6 
104.7 

104. 9 
^05.0 

105. 1 
105-3 
105.4 
105- 5 
105,7 

105.8 
105- 9 
106.0 
106.2 
106.3 

106.4 
106.6 

106. 7 
106.8 
107.0 



107.8 
107.9 



108.2 
108.3 



108.9 

109. 1 
109. 2 
109- 3 
109- 5 



190.6 



286. ( 



476.6 



Hon. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .123 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



85 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
13° 



22. OO 
22. 02 
22.05 



22. IO 
22.13 
22. 15 
22. 18 

22. 21 
22.23 
22. 26 
22.28 
22.31 

22-34 
22.36 
22-39 
22.41 
22.44 

22.47 
22.49 
22.52 



22.65 
22.67 
22. 70 

22-73 
22.75 
22.78 
22.80 
22.83 

22.86 
22.88 

22.91 

22.94 

22. 96 



23.OI 

23- 04 

23.06 
23.09 

23.II 
23- '4 
23- 15 
23- '9 
23- 22 

23- 24 
23- 27 

23.29 
23- 32 
23- 34 

23- 37 
23- 40 
23- 42 
23- 45 



94-55 



43- 84 
43- 89 
43-94 
43-99 
44- 05 
44.1.0 

44- 15 
44.20 
44.26 
44- 3« 
44- 3* 



44.78 
44-83 
44-88 

44-93 
44-98 
45-04 
45-09 
45-14 

45- 19 

45-24 
45-30 
45-35 
45- 40 

45- 45 
45- 50 
45-55 
45.61 
45-66 



45.88 
45-92 

45-97 
46.02 
46.07 
46. 12 
46.18 

4623 
46.28 
46.30 
46.38 
46.43 

46.48 
46.54 
46.59 
46.64 
46.69 

46.74 
46.79 
46.84 
4690 



65.76 
65- 83 
65.91 
65- 99 
66.07 
66.15 

66.23 
66.30 
66.38 
66.46 
66.54 

66.62 
66.70 
66.77 
66.85 
66.93 

67.01 
67.09 
67.16 
67.24 
67- 32 

67.40 
67.48 
67- 55 
67.63 
67.71 

67.79 
67.86 
67.94 
68.02 
68. 10 

68.18 

68. 25 
68.33 
68.41 
68.49 

68.56 
68.64 
68.72 
68.81 
68.88 

68.95 
69.03 
69.11 

69. 18 
69.26 

69- 34 
69.42 
69.46 
69- 57 
69.65 

69- 73 
69.81 
69.88 
.69.96 
7004 

70. 1 1 



400 500 600 700 800 900 1100 



241.4 
241.7 
242.0 
242.2 
242.5 

242.8 
243-« 
243-4 
243-7 
244.0 

244- 3 
244.6 
244.8 
245- 1 
245- 4 

245-7 
246.0 
246.3 
246.6 
246.8 

247.1 
247.4 
247- 7 
248.0 
248.3 

248.6 
248.8 



250.0 
250.3 
250.6 
250.8 
251. 1 

2514 
25'- 7 
252.0 
252.3 
2525 

252.8 

253- P 
253- 4 
253- 7 

254- o 

254- 2 
254- 5 
254- 7 
255-1 
255- 4 

255- 7 
256.0 
256.2 
256.5 
256.8 

257- 1 
257-4 
257.6 
257-9 



1040 



Hor. dist. is for 30' point. Add or subtract .132 ft. to each 100 ft. of 
distance for each 10' departure. 



86 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
14° 



f 


100 


200 


300 


400 


500 


600 


700 


800 


900 


1100 


! 


o 


23-47 


47.00 


70.42 


93-9 


H7-4 


140.8 


164.3 


187.8 


211. 3. 


258.2 





J. 


23-5° 


47.00 


70.50 


94.0 


H7-5 


141. 


164.5 


188.0 


211. 5 


258. s 


1 


2 


23-52 


47-05 


70.58 


94.1 


117.6 


141. 2 


164.7 


188.2 


211.7 


258.8 


2 


3 


23-55 


47.10 


70.65 


94.2 


117.8 


I4I-3 


164.8 


188.4 


212.0 


259- 1 


3 


4 


23-58 


47-15 


70.73 


94-3 


117.9 


Hi- 5 


165.0 


188.6 


212. 2 


259-3 


4 


5 


23.60 


47.20 


70.81 


94.4 


118.0 


141.6 


165.2 


188.8 


212.4 


259.6 


5 


6 


23-63 


47-25 


70.88 


94-5 


Ii8. 1 


141. 8 


165.4 


189.0 


212.6 


259-9 


6 


7 


23-65 


47-31 


70.96 


94.6 


118.3 


141. 9 


165.6 


189. 2 


212.9 


260. 2 


7 


8 


23.68 


47-36 


71.04 


94-7 


118.4 


142. 1 


165.8 


189.4 


213.1 


260.5 


8 


9 


23.70 


47-41 


71.11 


94.8 


118.5 


142.2 


165-9 


189.6 


213-3 


260.8 


9 


IO 


23-73 


47.46 


71.19 


94-9 


118.6 


142.4 


166.1 


189.8 


213.6 


261.0 


10 


ii 


23. 76 


4751 


71.27 


95-0 


118. 8 


142.5 


166.3 


190.0 


,213- 8 


261.3 


M 


12 


23-78 


47-56 


71-34 


95- 1 


118.9 


142.7 


166.5 


190.2 


214.0 


261.6 


12 


13 


23.81 


47.61 


71.42 


95? 


119.0 


142.8 


166.6 


190.5 


214-3 


261.9 


13 


M 


23-83 


47.66 


7'- 50 


95-3 


119. 2 


143.0 


166.8 


190.7 


214-5 


262.2 


14 


»5 


23.86 


47-72 


71-57 


95-4 


H93 


143-2 


167.0 


190.9 


214.7 


262.4 


15 


16 


23.88 


47-77 


71.65 


95-5 


119.4 


143-3 


167.2 


191. 1 


215.0 


262.7 


16 


17 


23- 9i 


47.82 


71-73 


95-6 


119.6 


143-4 


167.4 


I9I-3 


215.2 


263.0 


17 


18 


23-94 


47.87 


71.80 


95-7 


119.7 


143-6 


167-5 


I9I-5 


215-4 


2633 


18 


19 


23.96 


47-92 


71.88 


95-8 


1 19. 8 


143-8 


167.7 


191.7 


215.6 


263.6 


19 


20 


23.98 


47-97 


72.00 


95-9 


119.9 


143-9 


167.9 


I9I-9 


215-9 


263.8 


ac 


31 


24.01 


48.02 


72.03 


96.0 


.120. 1 


144-1 


168. 1 


192. 1 


216. 1 


264. 1 


21 


22 


24.04 


48.07 


72. 11 


96.2 


120.2 


144.2 


168.3 


192.3 


216.3 


264.4 


22 


23 


24.06 


48. 12 


72. 19 


96. 2 


120.3 


144.4 


168.4 


192.5 


216.6 


264. 7 


23 


24 


24.09 


48.18 


72. 26 


96.4 


120.4 


144-5 


168.6 


192.7 


216.8 


265.0 


•24 


25 


24. " 


48.23 


72.34 


96.4 


120.6 


144-7 


168.8 


192.9 


217.0 


265.2 


25 


26 


24.14 


48.28 


72.42 


96.6 


120.7 


144.8 


169.0 


193- 1 


217.2 


265.5 


26 


27 


24. 16 


48.33 


72.49 


96.7 


120.8 


145- 


169. 2 


193- 3 


217-5 


265.8 


27 


28 


24.19 


48.38 


72.57 


96.8 


121. 


145- 1 


169- 3 


193- 5 


217.7 


266. 1 


28 


29 


24:22 


48.43 


72.64 


96.9 


121. 1 


145-3 


169.5 


193- 7 


217.9 


266.4 


29 


30 


24.24 


48.48 


72.72 


97.0 


121. 2 


145-4 


169.7 


193- 9 


218.2 


266.6 


30 


31 


24.27 


48.53 


72. 80 


97.1 


121.3 


145.6 


169.9 


194. 1 


218.4 


266.9 


3» 


32 


24.29 


48.58 


72.88 


97.2 


121. 5 


145-8 


170.0 


194-3 


218.6 


267.2 


32 


33 


24-32 


48.63 


72.95 


97-3 


121. 6 


145-9 


170.2 


194-5 


218.8 


267.5 


33 


34 


24-34 


48.68 


73-03 


97-4 


121. 7 


146.0 


170.4 


194.7 


219. 1 


267.8 


34 


35 


24-37 


48.74 


73- 10 


97-5 


121. 8 


146. 2 


170.6 


194-9 


219-3 


268.0 


35 


36 


24-39 


48.79 


73.18 


97.6 


122.0 


146.4 


170.8 


195- 1 


219-5 


268.3 


36 


37 


24.42 


48.84 


73-26 


97-7 


122. 1 


146.5 


170.9 


195-4 


219.8 


268.6 


37 


38 


24.44 


48.89 


73-33 


97.8 


122.2 


146.7 


171. 1 


195-6 


220.0 


268.9 


38 


39 


24.47 


48.94 


73-41 


97-9 


122.4 


146.8 


171-3 


195.8 


220. 2. 


269.2 


39 


•40 


24-50 


48.99 


73-48 


98.0 


122.5 


147.0 


I7I-5 


196.0 


220.4 


269.4 


40 


4» 


24-52 


49.04 


73.56 


98.1 


122.6 


147. 1 


171. 6 


196.2 


220.7 


269.7 


41 


42 


24-54 


49.09 


73-64 


98.2 


122.7 


I4Z-3 


171.8 


196.4 


220.9 


270.0 


42 


43 


24-57 


49.14 


73- 7i 


98.3 


122.8 


147-4 


172.0 


196.6 


221. 1 


270.3 


43 


44 


24.60 


49.19 


73-79 


98.4 


123.0 


147.6 


172.2 


196,8 


221.4 


270.6 


44 


45 


24.62 


49.24 


73-86 


98.5 


123. 1 


147-7 


172.4 


197.0 


221.6 


270.8 


45 


46 


24.65 


4929 


73- 94 


98.6 


123.2 


147-9 


172.5 


197.2 


221.8 


271. 1 


46 


47 


24.67 


49-34 


74.02 


98.7 


1234 


148.0 


172.7 


197-4 


222. 1 


271-4 


47 


48 


24.70 


49-39 


74.09 


98.8 


123- 5 


148.2 


172.9 


197.6 


222.3 


271.7 


48 


49 


24.72 


49-44 


74-17 


98.9 


123.6 


148.3 


173-1 


197.8 


222.5 


272.0 


49 


50 


24-75 


49-50 


74-24 


99.0 


123- 7 


148.5 


173.2 


198.0 


222.7 


272.2 


5° 


5i 


24.77 


49-55 


74-32 


99.1 


123.9 


148.6 


173-4 


'198. 2 


223.0 


272.5 


5i 


52 


24. 80 


49.60 


74-39 


99-2 


124.0 


148.8 


173-6 


198.4 


223.2 


272. a 


52 


53 


24.82 


49- 65 


74-47 


99-3 


124. 1 


148.9 


173-8 


198.6 


223.4 


273- 1 


53 


54 


24-85 


49.70 


74-55 


99-4 


124.2 


149.1 


173-9 


198.8 


223.6 


273-3 


54 


55 


24.87 


49-75 


74.62 


99-5 


124.4 


149.2 


174.1 


199.0 


223.9 


273.6 


55 


56 


24.90 


49.80 


74-70 


99.6 


124-5 


149.4 


174-3 


199.2 


224.1 


273-9 


56 


57 


24.92 


49- 85 


74-77 


99-7 


124. 6 


149.6 


174- 5 


199.4 


224-3 


274.-2 


57 


58 


24. 95 


49.90 


74-85 


99.8 


124.8 


149-7 


174.6 


199.6 


224.6 


274- 4 


58 


59 


24.98 


49-95 


74.92 


99-9 


124.9 


149.8 


174.8 


199.8 


224.8 


274.7 


59 


Horz. 
Dist. 


93-73 


187.5 


281.2 


374-9 


468.6 


562 


656 


750 


844 


1031 


Horz. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .141 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



87 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 

15° 



t 


100 


200 


300 


400 


500 


600 


700 


800 


900 


1100 


/ 


o 


25.00 


50.00 


75.00 


100.0 


125.0 


150.0 


I75-0 


200.0 


225.0 


275.0 


O 


1 


25.02 


50.05 


75.08 


100. 1 


125.2 


150.2 


175- 2 


200. 2 


225.3 


275-3 


1 


2 


25- 05 


50. 10 


75-15 


100.2 


125.2 


150.3 


175-4 


200.4 


225-5 


275-6 


2 


3 


25.08 


5«- 15 


75-23 


100.3 


125-4 


150.4 


175- 5 


200. 6 


225.7 


275-8 


3 


4 


25- 10 


50.20 


75-30 


100.4 


125-5 


150.6 


175-7 


200.8 


225.9 


276. 1 


4 


5 


25- '3 


50.25 


75-3 8 


100.5 


125.* 


150.8 


175- 9 


201.0 


226.1 


276.4 


5 


6 


25- 15 


50.30 


75-45 


100.6 


125.8 


150.9 


176.0 


201.2 


226.4 


276.6 


6 


7 


25. 18 


50.35 


75-53 


100.7 


125- 9 


1511 


176.2 


201.4 


226.6 


276.9 


7 


8 


25. 20 


30.40 


75.60 


100.8 


126.0 


151- 2 


176.4 


201.6 


226.8 


277.2 


8 


9 


25- 23 


50.45 


75.68 


100.9 


126. 1 


1514 


176.6 


201.8 


227.0 


277-5 


9 


IO 


25- 25 


50.50 


75- 76 


101.0 


126.3 


I5I-5 


176.8 


202.0 


227.3 


277-8 




ti. 


25.28 


50.55 


75.83 


IOI. I 


126.4 


151-7 


176. 9 


202.2 


227.5 


278.0 


11 


12 


25.30 


50.60 


75-9Q 


101.2 


126.5 


151.8 


177.1 


202.4 


227.7 


278.3 


12 


13 


25- 33 


50. 65. 


75-98 


101.3 


126.6 


152.0 


177-3 


202.6 


227.9 


278.6 


13 


»4 


25- 35 


50.70 


76.06 


101. 4 


126.8 


152.1 


177-5 


202.8 


228.2 


278.9 


14 


»5 


25- 38 


50-75 


76. 13 


101. 5 


126.9 


152.3 


177.6 


203.0 


228.4 


279.2 


15 


16 


25-4° 


50.80 


76.21 


101. 6 


127.0 


152.4 


177-8 


203.2 


228.6 


279. 4- 


16 


17 


25- 43 


50.85 


76.28 


101. 7 


127. 1 


152.6 


178.0 


203.4 


228.8 


279.7 


17 


18 


25-45 


50.90 


76.36 


101. 8 


127-3 


152.7 


178.2 


203.6 


229. 1 


280.0 


18 


19 


25-48 


50.95 


76.43 


101. 9 


127.4 


1529 


178.3 


203.8 


229.3 


280.2 


19 


20 


25- 50 


5«oo 


76.51 


102.0 


1275 


153- 


178.5 


204.0 


229.5 


280.5 


20 


21 


25-53 


5J05 


76.58 


102. 1 


127.6 


153- 2 


178.7 


204.2 


229.7 


280.8 


21 


22 


25- 55 


51.10 


76.66 


102.2 


127.8 


153- 3 


1789 


204.4 


230.0 


281.1 


22 


23 


25-58 


5115 


76.73 


102.3 


127.9 


153-5 


179.0 


204.6 


230.2 


281.2 


23 


24 


25.60 


51. -o 


76.81 


102.4 


128.0 


153-6 


179.2 


204.8 


230.4 


281.6 


24 


25 


25- 63 


51.25 


76.88 


102.5 


128.1 


153-8 


179- 4 


205.0 


230.6 


281.9 


25 


26 


25- 65 


51-30 


76.95 


102. 6 


128.3 


153-9 


179.6 


205.2 


230.9 


282.2 


26" 


27 


25.68 


51-35 


77- 03 


102.7 


128.4 


154- 1 


179- 7 


205.4 


231. 1 


282.4 


27 


28 


25.70 


51.40 


77.11 


102.8 


128.5 


154-2 


179.9 


205.6 


231- 3 


282.7 


28 


29 


25- 73 


51-45 


77-18 


102. 9 


128.6 


154-4 


180. 1 


205.8 


231-5 


283.0 


29 


30 


25-75 


5150 


77.26 


103.0 


128.8 


154-5 


180.3 


206.0 


231.8 


283- 3 


30 


3« 


25- 78 


51-55 


77-33 


103. 1 


128.9 


' 154-7 


180.4 


206.2 


232.0 


283.6 


31 


32 


25.80 


51.60 


77- 4i 


103.2 


129.0 


154-8 


180.6 


206.4 


232.2 


283.8 


32 


33 


25- 83 


51- 65 


77.48 


1033 


129.1 


i55-o 


180.8 


206.6 


232- 4 


284. 1 


33 


34 


25-85 


; 5i-70 


77-56 


1034 


129-3 


155- 1 


181.0 


206.8 


2327 


284.4 


34 


35 


25.88 


51-75 


77- 63 


103- 5 


129.4 


155-3 


181. 1 


207.0 


232.9 


284.6 


35 


36 


25- 90 


51.80 


77.70 


103.6 


129-5 


155-4 


181. 3 


207.2 


233- 1 


2849 


36 


37 


25-93 


51- 85 


77.78 


1037 


129. 6 


155-6 


181. 5 


207.4 


233-3 


285.2 


37 


38 


25-95 


51.90 


77- 85 


103.8 


129.8 


155-7 


181. 7 


207.6 


233- 6 


285.5 


38 


39 


25- 98 


51-95 


77-93 


103.9 


129.9 


155-9 


181.8 


207.8 


233- 8 


285.7 


39 


40 


26.00 


52.00 


78.00 


104.0 


130.0 


156.0 


182.0 


208.0 


234-0 


286.0 


40 


4i 


26.02 


52.05 


78.08 


104. 1 


130.2 


156.2 


182.2 


208.2 


234- 3 


286^3 


41 


42 


26.05 


52. 10 


78.15 


104.2 


130.2 


156.3 


182.4 


208.4 


234-5 


286.6 


42 


43 


26.08 


52.15 


78.23 


104.3 


130.4 


156.4 


182.5 


208.6 


234-7 


286.8 


43 


44 


26. 10 


52.20 


78.30 


104.4 


130-5 


156.6 


182.7 


208.8 


234-9 


287. 1 


44 


45 


26.12 


52.25 


78.38 


104- 5 


130.6 


1568 


182.9 


209.0 


235- 1 


287.4 


45 


46 


26.15 


52.30 


78.45 


104.6 


130- 8 


156.9 


183.0 


209.2 


235-4 


287.6 


46 


47 
48 


26.18 


52.35 


78.52 


1047 


130.9 


157- 


183.2 


209.4 


235- 6 


287.9 


47 


26. 20 


52.40 


78.60 


104.8 


131. 


157-2 


1834 


209.6 


235-8 


288.2 


48 


49 


26. 22 


52.45 


78.67 


104.9 


1311 


157-3 


183.6 


209.8 


236.0 


288.5 


49 


5° 


26.25 


52.50 


78.75 


105.0 


131-2 


157-5 


183-7 


210.0 


236.2 


288.7 


50 


5i 


26.27 


52.55 


78.82 


105.1 


131-4 


157-6 


183.9 


210.2 


236.5 


289.0 


51 


52 


26.30 


52.60 


78.90 


105.2 


131-5 


157-8 


184. 1 


210.4 


236. 7 


289.3 


52 


53 


26.32 


52.65 


78.97 


105- 3 


1316 


157-9 


184-3 


210.6 


236.9 


289. 6 


53 


54 


26.35 


52.70 


79.04 


1054 


131- 7 


158. 1 


184.4 


210.8 


237- 1 


289.8 


54 


55 


26.37 


52.74 


79.12 


105.5 


131- 9. 


158.2 


184.6 


211. 


237- 4 


290. 1 


55 


56 


26.40 


52.79 


79.19 


105.6 


1320 


158.4 


184.8 


211. 2 


237- 6 


290.4 


56 


57 
58 


26.42 


52.84 


79.27 


105- 7 


132. t 


158.5 


185.0 


211. 4 


237-8 


290.6 


57 


26.45 


52.89 


79-34 


105. 8 


132.2 


158.7 


185.1 


211. 6 


238.0 


290.9 


58 


59 


26.47 


52.94 


79.42 


1059 


1324 


158.8 


185.3 


211.8 


238.2 


291.2 


59 


Horz. 
Dist. 


92.86 


185.7 


278.6 


371-4 


464- 3 


557 


650 


743 


836 


1022 


Horz. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .150 ft. to each 100 ft. of 
distance for each 10' departure. 



88 



TOPOGRAPHIC STADIA SURVEYING 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
16° 



Horz. 
Dist. 



100 200 300 400 500 600 700 800 900 



26.50 
26.52 
26.55 
26.57 
26.60 
26.62 

26.64 
26.67 
26.69 
26.72 
26.74 

26.77 
26.79 
26.82 
26.84 
26.86 

26.89 

26. 91 
26.94 
26.96 
26.99 

27.01 
27.04 
27.06 
27.09 
27." 

27- 13 
27. 16 

27. 18 
27.21 
27.23 

27.26 
27.28 
27.30 
27-33 
27-35 

2738 
27.40 
27-43 
27-45 
27.48 

27.50 
27.52 
2755 
27-57 
27.60 

27.62 
27- 65 
27.67 
27.69 
2772 

27.74 
27- 77 
27.79 
27.82 
27- 84 

27.86 
27.89 
27.91 
27.04 



9«-93 



5299 
53- 04 
53- 09 



53-24 

53-29 
53-34 
53-39 
53-44 
53- 48 

53-53 
53- 58 
53-63 
53-68 
53-73 

53- 78 
53-83 



54.02 
54- 07 
54- >2 
54- 17 
54-22 

54 26 
54-32 
54-37 
54-41 
54- 46 

54- 5 1 
54- 56 
54 61 
54-66 
54- 71 

54- 76 
54.80 
54- 85 
54- 90 
54-95 



55- 19 

55- 24 
55-29 
55-34 
55-39 
55-44 

55- 48 
55-53 
55- 58 
55- 63 
55-68 

55-73 
55- 78 
55-82 
-55- 87 



79-45 
79- 56 
79.64 
79- 7 1 
79.78 
79.86 

79.90 
80.01 
80.08 
80. 15 
80., 23 

80.30 
80.38 
80.45 
80.52 
80.60 

80.67 
80.74 



81.62 
81.70 

8i.77 
81.84 
81.92 
81.99 
82. 10 

82.13 

82. 21 
82.28 
82.35 
82.43 

82.50 
82.57 
82.60 
82.72 
82.79 

82.86 
82.94 
8301 
83.08 
83.15 

83- 23 
83-3° 
83- 37 
83-44 
83- 52 

83- 59 
83.66 
83-74 
83.81 



275-8 



Horz. 
Dist. 



Hor. dist. is for 30' point. Add or subtract .158 ft. to each 100 ft. of 
distance for each 10' departure. 



TOPOGRAPHIC STADIA SURVEYING 



89 



Table 7 — Continued 

DIFFERENCES IN ELEVATION 
17° to 33° 



t 


17° 


18° 


19° 


20° 


21° 


22° 


23° 


v 9 


o 


27. 96 


29- 39 


30.78 


32.14 


33- 46 


34-73 


35-97 


-0 


I 


27.99 


29.42 


30.81 


32.16 


33- 48 


34-75 


35-99 


• 


2 


28. 01 


29.44 


30.83 


32- 18 


33- 50 


34-77 


3601 


2? 


3 


28.04 


29- 47 


30.85 


32.21 


33- 52 


34-8o 


3603 


3 


4 


28.06 


29.49 


30.87 


32- 23 


33-54 


34.82 


36.05 


4 


5 


28.08 


29- 5 1 


30.90 


32.25 


33-57 


34- 84 


36.07 


5 


6 


28. 10 


29- 53 


30.92 


32.27 


33V59 


34-86 


36.09 


6 


7 


28.13 


29.56 


30.94 


32.30 


33,6i 


34.88 


36.11 


7 


8 


28.15 


29- 58 


30.97 


32.32 


33- 63 


34-90 


36.13 


8 


9 


28.18 


. 29.60 


3099 


32.34 


33- 65 


34-92 


36.15 


9 


to 


28.20 


29.62 


31.01 


32.36 


3,3- 67 


34-94 


36.17 


10 


II 


28.22 


2965 


31.04 


■ 32. 39 


33- 70 


34- 96 


36.19 


11 


12 


28.25 


29.67 


31.06 


3241 


33-72 


3498 


36.21 


12 


«3 


28.27 


29.69 


3108 


32.43 


, 33- 74 


35- 00 


36.23 


13 


•4 


28.30 


29.72 


31. 10 


32.45 


33- 76 


35- 02 


36.25 


I* 


«5 


28.32 


29- 74 


31- 13 


3247 


33- 78 


35- 05 


36.27 


IS 


16 


• 28.34 


29.76 


3i- 15 


32.49 


33- 80 


35- 07 


3629 


16 


«7 


.28.37 


29.79 


3i. <7 


32.51 


33-82 


35- 09 


46.31 


17 


It 


28.39 


29.81 


3i- 19 


32.54 


33- 84 


35-n 


36.33 


18 


»9 


28.42 


29- 83 


31-22 


32- 56 


33- 87 


35- 13 


36.35 


19 


20 


28.44 


29.86 


3i- 24 


32.58 


33- 89 


35- 15 


36.37 


20 


31 


28.47 


29.88 


31-26 


32.61 


33- 9> 


35- 17 


36.39 


21 


22 


28.49 


29.90 


3'- 28 


32.63 


33-93 


35- 19 


36.41 


22 


23 


28.51 


29- 93 


3»-3o 


32.65 


33-95 


35-21 


36.43 


23 


24 


28.54 


29- 95 


3'- 33 


32.67 


33-97 


35-23 


36.45 


24 


«5 


28.56 


29.97 


3i- 35 


3270 


33-99 


35-25 


36.47 


25 


26 


28.58 


30.00 


31-38 


32.72 


34- 01 


35- 27 


36.49 


26 


V} 


28.61 


30.02 


3«-40 


32.74 


34- 04 


35-29 


36-5J 


27 


2a 


■ 28.63 


30.04 


3i. 42 


32-76 


34- 06 


35-31 


36.53 


28 


29 


28.66 


30.07 


3'-43 


3278 


34.08 


35-34 


36.55 


29 


30 


28. 68 


30.09 


3i- 47 


32.80 


34- 10 


35- 36 


36.57 


JO 


3i 


28.70 


30.11 


3»-49 


32.83 


34- 12 


35- 38 


36.59 


3» 


32 


28.73 


30.14 


3I-5I 


32.85 


34- «4 


35- 40 


36.61 


32 


33 


28.75 


30. 16 


3>-54 


32.87 


34- 16 


35-42 


36.63 


33 


34 


28.77 


30.19 


31-56 


32.89 


34- 18 


35-44 


36.65 


34 


35 


28.80 


30.21 


31-58 


32.91 


34-21 


35- 46 


36.67 


35 


36 


28.82 


30.23 


3160 


32.93 


34-23 


35- 48 


36.69 


36 


37 


28.85 


30.26 


3>-63 


32.96 


34- 25 


35- 50 


36.71 


37 


38 


28.87 


30.28 


3i- 65 


32.98 


34- 27 


35-52 


36.73 


38 


39 


28.89 


30.30 


31-67 


33- 00 


34- 29 


35-54 


36.75 


39 


40 


28.92 


30.32 


3i- 69 


33- 02 


34-31 


' 35- 56 


36.77 


40 


4« 


28.94 


30.36 


31-72 


33- 05 


34- 33 


35- 58 


36.79 


41 


42 


28.96 


30.37 


31-74 


33-07 


34-35 


35-6o 


36.80 


42 


43 


28.99 


30.39 


3i- 76 


33- 09 


34- 38 


35-62 


36.82 


43 


44 


29.01 


30.41 


3i- 78 


33 1 1 


34- 40 


35- 64 


36.84 


44 


45 


29.04 


3044 


3<-8i 


33- «3 


34- 42 


35-66 


36.86 


45 


46 


29.06 


30.46 


31-83 


33- '5 


34-44 


35-68 


36.88 


46 


47 


29.08 


30.49 


31.85 


33- '8 


34-46 


35- 70 


36.90 


47 


48 


29.11 


3051 


3187 


33- 20 


3448 


35-72 


36.92 


48 


49 


29.13 


30.53 


3>-90 


33- 32 


34- 50 


35-74 


36.94 


49 


50 


29- "5 


30.55 


3«-92 


33-24 


34-52 


35- 76 


36.96 


50 


5' 


29. 18 


30.58 


31-94 


33-26 


34-54 


35- 78 


36.98 


5* 


52 


29. 20 


30.60 


31.96 


33,28 


34-57 


35-8o 


37.00 


52 


53 


29.23 


30.62 


31-99 


33-31 


34-59 


35- 83 


37.02 


53 


54 


29.25 


30.65 


32.01 


33-33 


34-6i 


35- 85 


37- 04 


54 


55 


29.27 


30. 67 


32.03 


,33- 35 


34- 63 


35- 87 


37- 06 


55 


56 


29.30 


30.69 


32- 05 


33-37 


34- 65 


35- 89 


37.o8 


56 


57 


29.32 


30.72 


32.07 


33-39 


34- 67 


35-91 


37-IO 


57 


58 


29- 34 


30.74 


32.09 


33- 4> 


34- 69 


35-93 


37.12 


58 


59 


29- 37 


30.76 


32.12 


33-44 


34-71 


35-95 


37- 14 


59 


Horz. 
Dist. 


90.96 


89. 93 


88.86 


87.74 


86-57 


85-36 


84. 10 


Horz. 
,Dist. 


Horz. 
Corr. 


.167 


.175 


.182 


.191 


.198 


.206 


.213 


Horz. 
Corr. 



Hor. correction is for 10' each way from the 30' point- 
All Values are for a Rod Reading of roo ft. 



90 



TOPOGKAPHIC STADIA SURVEYING 



Table 7 — Concluded 

DIFFERENCES IN ELEVATION 
34° to 29° 



# 


240 


25° 


26 d 


27° 


28° 


29*5 


f 


o 


37.16 


38.30 


39-49 


40.45 


41-45 


42.40 


0. 


f 


37.18 


38.32 


39-42 


40.47 


41.47 


42.42 


1 


2 


,37.20 


38.34 


39-44 


40.49 


41.48 


42-43 


1 


3 


. 37-22 


38.36 


39-46 


40.51 


41.50 


42.45 


3 


4 


37.23 


38.38 


39-47 


40.52 


41-52 


42.46 


4 


5 


37.25 


38.40 


39-49 


40.54 


41-54 


42.48 


S 


6 


37- 27 


38.41 


39- 5* 


40.55 


41-55 


42.49 


6 


7 


37-29 


38.43 


39- 5i 


40.57 


41-57 


42.51 


7 


8 


37.31 


38.45 


39-55 


40.59 


41.58 


42-53 


& 


9 


37-33 


38.47 


39- 56 


40. 61 


41.60 


42-54 


9 


IO 


37-35 


38.49 


39- 58 


40.62 


41.61 


4256 


10 


ii 


37-37 


38.52 


39- 60 


40.64 


41.63 


42.58 


it 


12 


; 37-39 


38.53 


39.61 


40.66 


41.65 


42-59 


12 


•3 


37- 41 


38.55 


' 39- 63 


40.68 


41.67 


42.60 


il 


«4 


37-43 


38.56 


•39-65 


40. 69 


41.68 


42.62 


14 


*5 


37-45 


35-58 


39- 67 


40.71 


41.70 


42.64 


IS 


16 


37- 47 - 


38. bo 


39- 69 


40.72 


41.71 


42.65 


16 


•7 


37-49 


38.62 


39-71 


4074 


41-73 


42.66 


17 


18 


37-51 


■38. 64 


39-72 


40.76 


41- 74 


42.68 


18 


19 


37-53 


38.66 


39-74 


40.78 


41.76 


42.70 


19 


20 


3754 


.38.67 


. 39- 76 


4079 


41-77 


4271 


20 


21 


37- 56 


•38.69 


39.78 


40.81 


41-79 


42.72 


21 


22 


37.58 


38.7J 


39-79 


40.82 


41.81 


42.74 


22 


23 


37-6o 


•38.73 


39.82 


40.84 


41.83 


42.76 


23 


24 


37.62 


38.75 


39-83 


40.86 


41.84 


42.77 


24 


25 


37- 64 


38.76 


39-85 


40.88 


41.86 


42.78 


25 


26 


37.66 


38.78 


*39-86 


40.89 


41.87 


42. 80 


26 


27 


37.68 


38.80 


39.88 


40.91 


41.89 


42.82 


27 


28 


37- 70 


38-82 


39.90 


40.92 


41.90 


42.83 


28 


29 


37-72 


38.84 


39- 92 


20.94 


41.92 


42.85 


29 


30 


37-74 


38.86 


39-93 


40.96 


4i- 93 


42.86 


30 


31 


37- 76 


38.88 


39-95 


40.98 


41-95 


42.88 


3» 


32 


37-77 


38.89 


39-97 


4099 


41-97 


42.89 


32 


33 


37-79 


38.9' 


39-99 


41.01 


41.99 


42.91 


33 


34 


37-8i 


38.93 


40.00 


41.02 


42.00 


42.92 


34 


35 


37- 83 


38. 95 


40.02 


.41.04 


42.02 


42.94 


35 


36 


37.85 


38.97 


40.04 


41.06 


42.03 


42-95 


36 


37 


37- 87 


38.99 


40.06 


41.08 


42.05 


42.97 


37 


38 


37.89 


39- 00 


40.07 


41.09 


42. 06 


42.98 


38 


39 


37- 9i 


39- 02 


40.09 


41.11 


42.08 


43.00 


39 


40 


37-93 


39- 04 


40.11 


41.12 


42.09 


43.01 


40 


4i 


37-95 


39- 06 


40.13 


41.14 


42.11 


43- 03 


4i 


42 


37-96 


39.08 


40.14 


41. 16 


42. 12 


43- 04 


4* 


43 


37- 98 


39- 10 


40. 16 


41.18 


42. 14 


43- 06 


43 


44 


38.00 


39-" 


40. 18 


41.19 


42.15 


43- 07 


44 


45 


38.02 


39- 13 


. 40.20 


41.21 


42.17 


43- 09 


45 


46 


38.04 


'39. 15 


40.21 


41.22 


42.19 


43. 10 


46 


47 


38.06 


39- 17 


40.23 


41.24 


42. 21 


43-12 


47 


48 


38.08 


39-i8 


40.24 


41.26 


42. 22 


43- 13 


48 


49 


38.10 


39- 20 


40. 26 


41.28 


42.24 


43-15 


49 


SO 


38. n 


39- 2? 


40.28 


41.29 


42.25 


43.16 


50 


5i 


38.13 


39.24 


40.30 


41-31 


42.26 


43- 17 


5« 


52 


38.15 


39.26 


40.31 


41-32 


42.28 


43.18 


52 


53 


38.17 


39-27 


40.33 


41-34 


42.30 


43.20 


53 


54 


38.19 


39-29 


40-35 


41-35 


42-31 


43-21 


54 


55 


38.21 


39- 3i 


40- 37 


41-37 


42.33 


43-23 


55 


56 


38.23 


39-33 


40.38 


41-39 


42.34 


43-24 


56 


57 


38.25 


39- 35. 


40.40 


41.41 


42.36 


43.26 


57 


58 


38.26 


39- 36 


40.42 


41.42 


42.37 


43- 27 


58 


59 


38.28 


39-38 


40.44 


41-43 


42-39 


43- 29 


59 


'Horz. 
Dist.. 


82.80 


8 1. .47 


80.09 


78.68 


.77-23 


75-75 


Horz. 
Dist. 



Horz. 
Corr. 



.238 



„ Horz. 
• 2 S° Corr. 



Hor„ correction 5s for 10' each way from the 30' point. 
All Values are for a Rod Reading of 100 ft. 



TOPOGRAPHIC STADIA SURVEYING 91 

Conversion of Feet to Decimals of a Mile. 

Table 8 is a table for the conversion of feet to decimals of a 
mile. A table of this character will be found convenient 
when the mile is the unit for platting. This table is repro- 
duced by permission from publications of the U. S. Geological 
Survey. 

For any distance expressed in feet which is likely to come 
into consideration in making a stadia survey the equivalent 
fraction of a mile is noted. 



92 



TOPOGRAPHIC STADIA SURVEYING 



Table 8 

CONVERSION OF FEET TO DECIMALS OF A MILE 
(By permission of the U. S. Geological Survey) 



Feet. 


Mile. 


Feet. 


Mile. 


Feet. 


Mile. 


Feet. 


Mile 


Feet. 


Mile. 


Feet. 


Mile. 


Feet. 


Mile. 


IOO 


0.019 


600 


0. 114 


1 100 


0. 208 


1600 


0.303 


2100 


0.398 


2600 


.492 


3100 


0.587 


IO 


.021 


10 


.116 


10 


.210 


10 


• 305 


10 


.400 


10 


.494 


10 


•589 


20 


.023 


20 


.118 


20 


. 212 


20 


• 307 


20 


.402 


20 


496 


20 


•59i 


30 


.025 


30 


. 120 


30 


.214 


30 


• 309 


30 


.404 


30 


498 


30 


•593 


40 


.026 


40 


. 122 


40 


.216 


40 


•3" 


40 


• 405 


40 


500 


40 


•595 


50 


.028 


50 


.124 


50 


.218 


50 


•313 


50 


.407 


50 


502 


50 


•596 


60 


.030 


60 


•125 


60 


. 219 


60 


.314 


60 


.409 


60 


504 


60 


.598 


70 


.032 


76 


.127 


70 


.221 


70 


.316 


70 


.411 


70 


506 


70 


.600 


80 


•034 


80 


.129 


80 


.223 


80 


.318 


80 


• 413 


80 


508 


80 


.602 


90 


.036 


90 


•131 


90 


.225 


90 


.320 


90 


•415 


90 


509 


90 


.604 


200 


.038 


700 


•133 


1200' 


.227 


1700 


.322 


2200 


.417 


2700 


5ii 


3200 


.606 


10 


.040 


10 


•134 


10 


. 229 


10 


•324 


IO 


.419 


10 


5i3 


10 


.608 


20 


.042 


20 


.136 


20 


.231 


20 


.326 


20 


.420 


20 


5i5 


20 


.610 


30 


.044 


30 


.138 


30 


• 233 


30 


.328 


30 


.422 


30 


5i7 


30 


.612 


40 


. 046 


40 


. 140 


40 


•235 


40 


••330 


40 


.424 


40 


519 


40 


.614 


50 


.047 


50 


.142 


50 


.236 


50 


•33i 


50 


.426 


50 


521 


50 


.616 


60 


.049 


60 


.144 


60 


.238 


60 


•333 


60 


.428 


60 


523 


60 


.617 


70 


.051 


70 


.146 


70 


• . 240 


70 


•335 


70 


•430 


70 


525 


70 


.619 


80 


•053 


80 


.148 


80 


.242 


80 


•337 


80 


•432 


80 


527 


80 


.621 


90 


•055 


90 


.150 


90 


.244 


90 


•339 


90 


•434 


90 


529 


90 


.623 


300 


•057 


800 


•152 


1300 


.246 


1800 


. -341 


2300 


•436 


2800 


530 


3300 


.625 


10 


•059 


IO 


•153 


xo 


.248 


- 10 


•343 


IO 


•438 


10 


532 


10 


.627 


20 


.061 


20 


•155 


20 


.250 


20 


• 345 


20 


•439 


20 


534 


20 


.629 


30 


. 062 


30 


•157 


30 


.252 


30 


•347 


30 


.441 


30 


536 


30 


.631 


40 


.064 


40 


•159 


40 


•254 


40 


•349 


40 


•443 


40 


538 


40 


.633 


50 


.066 


50 


.161 


50 


.256 


50 


•350 


50 


•445 


50 


340 


50 


.644 


60 


.068 


60 


.163 


60 


•257 


60 


•352 


60 


•447 


60 


542 


60 


.666 


70 


. 070 


70 


.165 


70 


.259 


70 


•354 


70 


•449 


70 


544 


70 


.688 


80 


.072 


80 


.167 


80 


.261 


80 


•356 


80 


•45i 


80 


546 


80 


.640 


90 


•074 


90 


.169 


90 


.263 


90 


•358 


90 


•453 


90 


547 


90 


.642 


400 


.076 


900 


.170 


1400 


• 265 


1900 


.360 


2400 


•455 


2900 


549 


3400 


•644 


10 


.078 


IO 


.172 


IO 


.267 


10 


.362 


IO 


•456 


10 


55i 


10 


.646 


20 


.080 


20 


.174 


20 


. 269 


20 


•364 


20 


•458 


20 


553 


20 ' 


.648 


30 


.082 


30 


.176 


30 


•271 


30 


.366 


30 


. 460 


30 


555 


30 


.650 


40 


.084 


40 


.178 


40 


. -273 


40 


.367 


40 


.462 


40 


557 


40 


.652 


50 


.086 


50 


.18O 


50 


•275 


50 


•369 


50 


.464 


50 


559 


50 


.653 


60 


.088 


60 


.181 


60 


.276 


60 


•37i 


60 


.466 


60 


56i 


(m 


•655 


70 


.089 


70 


.183 


70 


.278 


70 


•373 


70 


.468 


70 


562 


70 


' .657 


80 


• 091 


80 


.185 


80 


.280 


80 


•375 


80 


•470 


80 


564 


80 


•659 


90 


•093 


90 


.187 


90 


.282 


90 


•377 


90 


.472 


90 


566 


90 


.661 


500 


•o95 


IOOO 


. 189 


1500 


.284 


2000 


•379 


2500 


•474 


3000 


568 


35oo 


.663 


10 


.097 


IO 


.191 


IO 


.286 


10 


.381 


IO 


•475 


10 


57<> 


10 


.665 


20 


.098 


20 


•193 


20 


.288 


20 


.383 


20 


•477 


20. 


572 


20 


.667 


30 


. 100 


30 


•195 


30 


. 290 


30 


.384 


30 


•479 


30 • 


574 


30 


.669 


4° 


■ 162 


40 


.197 


40 


.292 


40 


.386 


40 


.481 


40 


576 


40 


.670 


50 


.104 


50 


.199 


SO 


.294 


50 


.388 


50 


-483 


50 


578 


50 


.672 


• 60 


. 106 


60 




60 


•295 


60 


•390 


60 


•485 


60 


58. . 


60 


.674 


70 


.108 


70 


' . 202 


70 


.297 


70 


•392 


70 


.487 


70 


581 


70 


.676 


80 


.•no 


80 


. 204 


80 


, -299 


80 


•394. 


80 


1 .489 


80 


'583 


80 


.678 


90 


. 112 


90 


.206 


90 


• .301 


90 


•396 


| 9° 


•491 


90 . 


583 


90 


.680 



CHAPTER IX 

HOW TO USE THE STADIA DIAGRAM 

Formulas and the Diagram. The diagram for the reduc- 
tion of stadia notes which accompanies this manual, is pre- 
pared specifically as a graphic solution at one operation of 
the approximation formulas: 

D = (r+e) cos 2 a; (27) 

and 

h = (r +e) sin a cos a (28) 

But the diagram may also be used in ascertaining the values 
of r cos 2 a and r sin a cos a in the correct formulas (Eq. 17) 
and (18) and for the approximation of (r+1) cos 2 a and (r+1) 
sin a cos a in formulas (29) and (30). As the formulas (17) 
and (18) need only be used for sights to turning points and 
on surveys requiring more than ordinary precision, it would 
seem advisable to give preference to reduction tables when- 
ever such approximation formulas as (27) and (28), or (29) 
and (30) will not serve. 

To Use the Diagram: Follow the angle ray which corre- 
sponds to the angle a of elevation or depression, to its inter- 
section with the curved line which corresponds to the value 
(r+e) in formulas (27) and (28). Holding a needle point 
at the intersection thus determined read off by the aid of 
the vertical lines the horizontal distance D, that is (r +e) cos 2 a 
and by the aid of the horizontal lines the difference in eleva- 
tion h, that is (r+e) sin a cos a. 

Or make the more convenient determination sufficiently 
93 



94 TOPOGRAPHIC STADIA SURVEYING 

close in all ordinary cases, by entering the diagram with 
(r+1) instead of (r+e). 

Whenever the use of the approximation formulae are per- 
missible, as in the determination of topography, the diagram 
gives, at once, the distance and the difference in elevation, 
for any rod-readings and any vertical angles within their 
scope. Distance should be read to the nearest foot and differ- 
ence in elevation to the nearest tenth of a foot. 

When points are located by the intersection of sights from 
two instrument stations, the horizontal distances from each 
of these two stations are scaled frcm the map. The diagram 
is now entered with each of these distances and needle points 
are placed at the intersections of these distances with the 
corresponding angle rays of the measured angles of elevation 
or depression. If the same difference in elevation is not 
indicated by both needle points the mean value should be 
recorded. 

The author, early in his experience on topographic surveys, 
constructed a diagram as here described based on the funda- 
mental approximation formulae (27) and (28) and has found 
the same a great convenience, fulfilling every requirement 
both as to minimizing mental effort, reducing the chance of 
error and insuring accuracy of results. It eliminates the 
undesirable features of many of the other diagrams at various 
times suggested for use, which do not give final results with- 
out additions or subtractions. 

The explanatory notes for the use of the diagram are as 
follows: 



D = (r +e) cos 2 a 

or 
h = (r +e) sin a cos a 



TOPOGRAPHIC STADIA SURVEYING 95 

STADIA DIAGRAM 

For Instruments rated 1 to 100 
Graphical Solution of the Approximation Formulas: 

D = (r+1) cos 2 a 
h = (r+l) sin a cos a 
Where 

r = reading on a vertical rod. 
a = vertical angle. 
D = horizontal distance. 
h = difference in elevation. 

e= instrument constant = the distance of the outside 
focal point of the object lens from the instrument axis. 

Directions: 

Follow the vertical angle ray to the curved line (r+e) or 
(r +1), as the case may be, and read D on the horizontal scale 
and In on the vertical scale. 

Note. — The diagram can also be used to find the value of 
r cos 2 a and of r sin a cos a. 



INDEX 



PAGE 

Accuracy of stadia surveys 48 

Alidade, vertical angles measured with 44 

Anallatic point, defined \ 2 

Anderson's stadia reduction table, explanation 63 

Approximation formulas for distance and difference in 

elevation 16 

Casgrain, W. T., and A. Noble, publication by, referred to. . 27 
Corrections, tables of, for departure of the stadia rod from 

a true vertical position 49, 50 

Corrections, tables of, when sighting point does not bisect 

the intercept 41, 46 

Cross-hairs, adjustable or fixed 1 

Departures from ordinary practice in stadia surveying 30 

Diagrams for stadia reduction 19, 22, 93 

Diagram furnished with manual 22 

Diagrammatic solution of stadia formulas 19 

Diagram with manual, how to use 22, 93 

Error, due to inclined rod 47 

Error, when sighting point does not bisect the intercept. ... 44 

Feet, conversion into miles, table 91 

Focal distance, principal, defined 3 

Formula, the stadia 9 

Formulas, basic 3 

Formulas for inclined sights 12 

Formulas for inclined sights, approximation 16 

Formulas, modification of, for slide-rule work 24 

Formulas, use of 17 

Hall, Wm. Hammond, referred to 30 

Height of telescope above station plug can be eliminated 

from notes 35 

Inclined sights, approximation formulas 16 

Inclined sights, formulas 12 

Instrument constant 2, 10 

97 



98 INDEX 

PAGE 

Intercept, defined 2 

Lietz, A. Co., referred to 34 

Lietz, A., paper on the Porro telescope 6 

Magnetic needle, surveys with use of 28, 37 

Magnetic needle, surveys without use of , 26 

Methods of stadia surveying 26 

Miles, conversion into feet . 91 

Noble, A., and W. T. Casgrain, publication by, referred to . 27 

Porro telescope 5 

Porro telescope, described by A. Lietz 6 

Rating factor 10 

Rating factor, defined 3 

Rating factor, determination of 10 

Refraction, the effect of 51 

Rod reading, defined 2 

Rod, special type of 30 

Rod, the target 2 

Rod, the telemeter or stadia, defined 2 

Sighting point, defined 2 

Slide-rule as an aid in reducing stadia work 24 

Stadia formula 9 

Stadia formulas, diagrammatic solution 19 

Stadia field notes 38 

Stadia field notes, sample pages 40 

Stadia notes, the platting of 52 

Stadia reduction diagrams 19, 22, 93 

Stadia reduction diagram, special type of, how to use. ... 22, 93 
Stadia reduction table, Anderson's, by permission of U. S. 

Geol. Survey, explanation 63 

Stadia reduction table, for readings of 100 feet and instru- 
ments rated 1 to 100, explanation of 55 

Stadia reduction with aid of slide-rule 24 

Stadia rod, defined 2 

Stadia surveying, methods of 26 

Stadia surveying, with use of magnetic needle 28, 37 

Stadia surveying, without use of magnetic needle 26 

Stadia surveys, accuracy of . . . 48 

Stadia surveys, reference to Noble and Casgrain 27 

Stadia unit, defined 3 



INDEX 99 



Tabled 

PAGE 

1. Corrections for too large a vertical angle 45 

2. Corrections for too small a vertical angle 46 

3-4. Corrections for departure of rod from a true vertical. 49, 50 

5. Values of e cos a and e sin a 54 

6. Stadia reduction table for a rod reading of 100 ft 55 

7. Stadia reduction table, U. S. Geol. Survey (Anderson). 63 

8. Conversion of feet into miles 91 

Tachymetry, defined 1 

Telemeter constant, defined 2 

Telemeter, defined 1 

Telemeter or instrument constant 10 

Telemeter rod 2 

Telemeter rod, special type of. 30 

Telemeter surveys, accuracy of 48 

U. S. Geological Survey, reduction table 63 

Vertical angles, measured with alidade 44 

Von Geldern, Otto, referred to , , 55 






JL ^ yr-irxJu 



IT